My main motivation for this one is to demonstrate a hybrid style of play and encourage some discussion.
I'm playing as Elizabeth who's been my favourite leader from the original Civ release due to her unrivalled research abilities with both the power economic traits. Unpatched warlords 2.08, Deity, Fractal, Normal speed, all standard settings.
Prior to this game I got wiped out twice by early-midgame AI attacks on the same settings. Thanks, Shaka and Asoka.
For some reason, I seem to roll better than normal starts at deity. I don't reroll unless it's a clearly awful start with 1 cow and no river or something, which is hopeless. But the game likes to give me good positions anyway, then crush my hopes with a random AI attack.

As the gold southwest of London wasn't visible from where I started, I settled on the spot. With 3 food specials making it an early game settler/whip powerhouse I'm not going to complain. I may be able to pick up that gold later, and I can already see a promising 2nd city site on the plains hill SE of the warrior that will be able to work the Desert Hill Gold and feed it by farming that Floodplain.
Hopefully you've realized that the initial build and research shown in that screenshot are a joke. Worker first and research Agriculture -> AH to ramp up early production quickly is the one and only correct decision given this start. I can power out settlers quickly and put the 3rd city at a military resource.

Worker -> warrior -> settler powered out by 2 food specials, growing to 3 before the next settler now that the third food special is online. I researched BW after AH and it's just come in. The settler is enroute to the 2nd city site and the worker is preparing its farm. Being founded on a plains hill and having a FP farm available is nice as you can immediately build a warrior and the city is size 2 when it's done.
I am lucky to have two copper and ivory available as military resources, the one in my capital explaining why the blue circle at the beginning didn't pick out the southwest gold. Very nice start, only missing any further visible happy resources after the first two, so we will want to be in Hereditary Rule sooner rather than later.
I've met Brennus from the east, and Roosevelt's borders are barely visible in the west. Since Roosevelt has Buddhism but didn't found it, there is at least one more AI out there, good news for trading. I'm going to want to found a city upriver, and another to claim the second copper and ivory.

There's another oasis tile in the north as it turns out - nice for the Financial early game although it is strictly worse than a floodplain later. To my annoyance, what I thought were floodplains in the north actually turn out to be river deserts (??) but I don't notice this until later, so I took that site first with the intention of making it a specialized production city. I'm researching masonry now and York will borrow the marble from London too in the early going, maximizing my ability to utilize my specials while still using slavery in London.
Marble is a really good resource to have at Deity, and leads me towards the strategy of getting quick Literature and saving my forest to chop the Great Library in my capital, to get maximal use of the chopped hammers. I will combine it with National Epic and 2 scientists run off food specials which gives 45gpp and 83% Great Scientist chance.

Most of the early game techs are done now. Because of the WFYABTA limit it's better to research them yourself rather than getting them all from Alphabet trades. Roosevelt is moving a small archer stack through my territory, but his target seems to be that barbarian city to the northeast fortunately. With mysticism having been researched fairly late Stonehenge is hopeless, but I am fine with just building three monuments, which can just be whipped out if needed quickly anyway like at Hastings. With only marginal city sites left for the taking, I will now scout Roosevelt and see if he will be vulnerable to an axe rush.

New York - which looks somewhat misplaced unless there's some resource to the west I can't see - is lightly defended and the axe rush will officially be on. Size 9 already by 1120 BC? Sheesh. Anyway, this is a good time to whip important buildings such as granary and library in London and dump the overflow hammers into axes. I plan to hit hard and fast, then switch my capital on to Great Library the moment Literature is discovered and have my satellite cities continue unit production.
Since Nottingham has deserts rather than floodplains, I will put the oases to good use there, as well as in Hastings.

New York has walls. Therefore I go straight for it while the defences are light and just skip Chicago. Ok, it is really stupid that NY wasn't founded 1 tile northeast of its current position - Chicago has no food to work the gold with! However it's not worth razing and refounding a size 9 city.
Washington is going to be in the west, and once healed up I'll push straight on for it before too many defenders get trained and let my troops trained later take out Chicago. My axes near it are just destroying loose enemy archers rather than letting them camp in a city.
I traded Alpha for Iron Working with someone - No one will give mathematics though. Nottingham's iron makes up a little for the non-floodplains there, it will be a somewhat credible production city now and I will build Heroic Epic there once the current war is done.
Meanwhile literature comes in and I send my workers to chop 5 forests around London to get the great library. I wasn't able to trade for Mathematics, but oh well. My first great scientist builds an Academy in London, the great library + philo trait will get another one out quickly to bulb Philosophy shortly after I have Code of Laws.
About 9 axes take out Washington, but immediately after I do, suddenly there's a longbow and elephant in Chicago in about 400 BC... Since only a spear accompanies them I overrun them anyway with about 6 random units, then sign peace. I could sacrifice all my units to take another city maybe, but I decide I'd rather save them for use as military police since I have not captured any more Luxury resources.
Good thing I pressed straight for the big cities.

250 BC. Second GS is out to pop Philosophy. I went there via Code of Laws as I want to enable Civil Service too. National epic is almost done, Cottages going up in London and Hastings, Forests to be chopped in Nottingham for Heroic Epic, after which the city will go back to training more units for a second war to mop up the Americans.
Why not build National Epic in Washington with its insane food? That city has horrible production, and it would take too long to build. I would rather build Globe Theatre there for later draft/slavery abuse. Also, Globe + NE combo produces too many artists unless I have cultural victory in mind, which I don't.
I trade philosophy around for Construction, Monarchy, Currency and Calendar, not that calendar is any use right now. I'll take the revolt into HR and Bureaucracy when CS finishes, to save a turn of anarchy.

And here's the economy at 90% science, it's pretty heavily CE at this point, but yet with just two hired scientists I will have a 3rd GS out very shortly to help with education, then a 4th for printing press, 5th for chemistry...
I get liberalism in 325 AD taking nationalism. After making a couple of Elephants for the war I will start Taj Mahal in London using my Marble. Rather than whip, I will grow my population and build units the old fashioned way to make best use of the golden age. The AI (Asoka, who is point and tech leader) surprises me by showing up with nationalism too shortly, so I don't revolt to Free Religion yet for fear he might use the anarchy time to beat me to the wonder.
In the meantime I manage to use education/liberalism to get trades for Compass, Metal Casting, Machinery, Feudalism, Engineering, Optics, but this hits the dreaded WFYABTA limit. I am avoiding adopting any religion, I don't want to offend any AIs too much with three factions on the continent; but this hinders my trading somewhat because I don't have close friends either.
This ends the early game. It's unlikely that Washington will put up too much resistance to a followup attack with Medieval units. I don't really have great production cities, so I will be looking to use a combination of Cannons and Draft Redcoats after that to grab some more land from another AI.
I'm playing as Elizabeth who's been my favourite leader from the original Civ release due to her unrivalled research abilities with both the power economic traits. Unpatched warlords 2.08, Deity, Fractal, Normal speed, all standard settings.
Prior to this game I got wiped out twice by early-midgame AI attacks on the same settings. Thanks, Shaka and Asoka.
For some reason, I seem to roll better than normal starts at deity. I don't reroll unless it's a clearly awful start with 1 cow and no river or something, which is hopeless. But the game likes to give me good positions anyway, then crush my hopes with a random AI attack.

As the gold southwest of London wasn't visible from where I started, I settled on the spot. With 3 food specials making it an early game settler/whip powerhouse I'm not going to complain. I may be able to pick up that gold later, and I can already see a promising 2nd city site on the plains hill SE of the warrior that will be able to work the Desert Hill Gold and feed it by farming that Floodplain.
Hopefully you've realized that the initial build and research shown in that screenshot are a joke. Worker first and research Agriculture -> AH to ramp up early production quickly is the one and only correct decision given this start. I can power out settlers quickly and put the 3rd city at a military resource.

Worker -> warrior -> settler powered out by 2 food specials, growing to 3 before the next settler now that the third food special is online. I researched BW after AH and it's just come in. The settler is enroute to the 2nd city site and the worker is preparing its farm. Being founded on a plains hill and having a FP farm available is nice as you can immediately build a warrior and the city is size 2 when it's done.
I am lucky to have two copper and ivory available as military resources, the one in my capital explaining why the blue circle at the beginning didn't pick out the southwest gold. Very nice start, only missing any further visible happy resources after the first two, so we will want to be in Hereditary Rule sooner rather than later.
I've met Brennus from the east, and Roosevelt's borders are barely visible in the west. Since Roosevelt has Buddhism but didn't found it, there is at least one more AI out there, good news for trading. I'm going to want to found a city upriver, and another to claim the second copper and ivory.

There's another oasis tile in the north as it turns out - nice for the Financial early game although it is strictly worse than a floodplain later. To my annoyance, what I thought were floodplains in the north actually turn out to be river deserts (??) but I don't notice this until later, so I took that site first with the intention of making it a specialized production city. I'm researching masonry now and York will borrow the marble from London too in the early going, maximizing my ability to utilize my specials while still using slavery in London.
Marble is a really good resource to have at Deity, and leads me towards the strategy of getting quick Literature and saving my forest to chop the Great Library in my capital, to get maximal use of the chopped hammers. I will combine it with National Epic and 2 scientists run off food specials which gives 45gpp and 83% Great Scientist chance.

Most of the early game techs are done now. Because of the WFYABTA limit it's better to research them yourself rather than getting them all from Alphabet trades. Roosevelt is moving a small archer stack through my territory, but his target seems to be that barbarian city to the northeast fortunately. With mysticism having been researched fairly late Stonehenge is hopeless, but I am fine with just building three monuments, which can just be whipped out if needed quickly anyway like at Hastings. With only marginal city sites left for the taking, I will now scout Roosevelt and see if he will be vulnerable to an axe rush.

New York - which looks somewhat misplaced unless there's some resource to the west I can't see - is lightly defended and the axe rush will officially be on. Size 9 already by 1120 BC? Sheesh. Anyway, this is a good time to whip important buildings such as granary and library in London and dump the overflow hammers into axes. I plan to hit hard and fast, then switch my capital on to Great Library the moment Literature is discovered and have my satellite cities continue unit production.
Since Nottingham has deserts rather than floodplains, I will put the oases to good use there, as well as in Hastings.

New York has walls. Therefore I go straight for it while the defences are light and just skip Chicago. Ok, it is really stupid that NY wasn't founded 1 tile northeast of its current position - Chicago has no food to work the gold with! However it's not worth razing and refounding a size 9 city.
Washington is going to be in the west, and once healed up I'll push straight on for it before too many defenders get trained and let my troops trained later take out Chicago. My axes near it are just destroying loose enemy archers rather than letting them camp in a city.
I traded Alpha for Iron Working with someone - No one will give mathematics though. Nottingham's iron makes up a little for the non-floodplains there, it will be a somewhat credible production city now and I will build Heroic Epic there once the current war is done.
Meanwhile literature comes in and I send my workers to chop 5 forests around London to get the great library. I wasn't able to trade for Mathematics, but oh well. My first great scientist builds an Academy in London, the great library + philo trait will get another one out quickly to bulb Philosophy shortly after I have Code of Laws.
About 9 axes take out Washington, but immediately after I do, suddenly there's a longbow and elephant in Chicago in about 400 BC... Since only a spear accompanies them I overrun them anyway with about 6 random units, then sign peace. I could sacrifice all my units to take another city maybe, but I decide I'd rather save them for use as military police since I have not captured any more Luxury resources.
Good thing I pressed straight for the big cities.

250 BC. Second GS is out to pop Philosophy. I went there via Code of Laws as I want to enable Civil Service too. National epic is almost done, Cottages going up in London and Hastings, Forests to be chopped in Nottingham for Heroic Epic, after which the city will go back to training more units for a second war to mop up the Americans.
Why not build National Epic in Washington with its insane food? That city has horrible production, and it would take too long to build. I would rather build Globe Theatre there for later draft/slavery abuse. Also, Globe + NE combo produces too many artists unless I have cultural victory in mind, which I don't.
I trade philosophy around for Construction, Monarchy, Currency and Calendar, not that calendar is any use right now. I'll take the revolt into HR and Bureaucracy when CS finishes, to save a turn of anarchy.

And here's the economy at 90% science, it's pretty heavily CE at this point, but yet with just two hired scientists I will have a 3rd GS out very shortly to help with education, then a 4th for printing press, 5th for chemistry...
I get liberalism in 325 AD taking nationalism. After making a couple of Elephants for the war I will start Taj Mahal in London using my Marble. Rather than whip, I will grow my population and build units the old fashioned way to make best use of the golden age. The AI (Asoka, who is point and tech leader) surprises me by showing up with nationalism too shortly, so I don't revolt to Free Religion yet for fear he might use the anarchy time to beat me to the wonder.
In the meantime I manage to use education/liberalism to get trades for Compass, Metal Casting, Machinery, Feudalism, Engineering, Optics, but this hits the dreaded WFYABTA limit. I am avoiding adopting any religion, I don't want to offend any AIs too much with three factions on the continent; but this hinders my trading somewhat because I don't have close friends either.
This ends the early game. It's unlikely that Washington will put up too much resistance to a followup attack with Medieval units. I don't really have great production cities, so I will be looking to use a combination of Cannons and Draft Redcoats after that to grab some more land from another AI.