If you are having trouble with prince, try this.
You want 4-5 cities in the beginning. 2 should focus on hammers, the others should be commerce towns. There can be some splitting of roles here, but if you focus on on city specialization first, you will learn better how to hybridize a city later. All cities need good food sources. It is better to have greater distance upkeep penalties and have a few extra food than to be short on food and close to the capital. The commerce cities should have plenty of grasslands and in the best case, some flood plain. But 2 food resources plus a bunch of grassland is fine. A river is of course a big plus for a commerce city (and if you have flood plain, you got a river). Basically, don't worry too much about fast tech until you have production ... it is always better to have a strong military early than not, even if you don't put it to use immediately.
Once you have 2 production cities running, you crank out 2 or 3 more cities (or conquer them, just as good, actually better because you don't have to build expensive settlers and should get some free workers). Pick 2 or 3 commerce cities (must have decent food without a lot of irrigation), and build and work every cottage possible as early as possible.
On prince, 2 or 3 good commerce cities should keep you well ahead of the competition. You may be a little behind for a while, but by following the proper tech line and with good trading, you should have 4 or 5 techs more than everyone else before the modern era, and be mopping up bacwards civs with cavalry and cannon against longbowmen.
As for tech strategy, of course, the early worker techs you need to develop your capital come first. You want to pick up bronze working early for 3 reasons ... you need copper, you want to use slavery, and you want to chop wood. If you get BW and have no nearby copper, you have to assess the situation ... are barbarians a problem? You may have to get archery (a last resort really), better than that is to self research iron working because if you don't have copper, you will usually have iron. If you have horses, you can use chariots to control barbs, and skip archery (always skip archery if at all possible).
Is there a neighbor right next to you? Then you want an early war and if you don't have bronze, go for iron. even if you don't have bronze, but do have horses, it is often good to skip iron hoping to trade for it later. This brings us to the second tech priority after BW ... Alphabet. After you have the critical worker techs and BW, go straight to alphabet. This is because by getting alphabet, you can trade and fill in the techs you missed, and be further advanced than if you had researched them all yourself. The AI doesn't research writing and alphabet early, so you can use both to trade. Consider holding on to alphabet itself for a little while to keep the AI from trading amongst themselves.
More on tech. After alphabet, your main goal is Liberalism. This is for the free tech, and also because education is right on the way (universities and oxford). you might make a couple side tracks here depending on the game. One is to get calendar for the happiness resources, another is to get monarchy for hereditary rule (often better to just wait and trade for it and get calendar instead) a third is to grab music for the free GA.
You will grab printing press for +1commerce for all your villages and towns, then beeline to democracy. At this time you can run some very powerful civics. US will give you +1 hammer for all those towns you have made, I think it's free speech gives you even more commerce, and free religion is great happiness and science. With a financial civ, towns by a river will now have 9! commerce and a hammer!
Skip all those wonders. I would recommend building only the GL and the Hanging Gardens (optional) until mid-late game. You can do without stonehenge, oracle, great wall, pyramids, notre dame, parthenon, etc. Only build these under perfect circumstances. Otherwise, your production really should be towards military. National wonders are another story, and in my opinion tend to be much stronger than world wonders. Oxford is a must as soon as possible (whip them universities), Globe theatre is a production juggernaut ... that high food commerce city with 2 hammers production? Now it produces hammers as quick as it can grow by whipping because there is no unhappiness.
Summary:
Get production (2 cities, maybe 3)
Get Commerce (at least 2 cities completely devoted to cottages)
Skip wonders -> make axemen/swordsmen
Go to war as early as is profitable with that army of axes/swords
Follow the proper tech line and trade well
As for a leader, I think the easiest to play is Huayna Capac/Inca ... Financial + Aggressive is deadly. Free combat 1 for 2/3 of the game is huge, as is +1 commerce on virtually every square.
resources, build appropriate buildings (theatre, coliseum, market, forge, temples, etc.), etc.
