Without getting into too much detail, what are some of the common build orders at the start of a game and their advantages? Basically the first 40-50 turns in the capital, if that many. Also, do I ever need to manually set worked tiles at this phase in the game or will the AI pick the right ones?
EDIT: I'm a bit of a windbag so this is what I consider "not too much detail." That said I can easily start number crunching or talking about fishing starts...
Do not rely on the governor to pick tiles unless you want your city doing almost exactly what you DON'T want it to do.
Build orders fall apart rather rapidly outside of the window "what starting techs do I need" as Civ 4 is a fair bit more dynamic due to map generation and civs in play than something like Civ 6, where build orders are more weighty gambits that you can push for in pretty much any game. Only saying so because Civ6 is the only other TBS I've played with any extensiveness (well, and Civ Rev, which is super simple) and the RTS concept of build orders which I am very familiar with are not equivalent to TBS games' version.
But in a general sense, for as many maps/starts as possible:
-Worker first (15T)
-build Warriors while working highest food tiles and improving with your worker
-size 3, slow build a Settler. Continue to improve tiles during this
Advantages are it is consistent and will work for like 90-95% of starts barring extenuating circumstances like Fishing start, gets you a worker ASAP to start improvements, and gives a decent first settler time (anywhere from 32-40ish) regularly. Disadvantages are it's highly dependent on your starting techs and tiles how rapidly you can pick up going forward.
-Worker first (15T)
-grow on warriors while teching Bronze Working ASAP
-size 4 start settler, chop/whip to completion or whip for overflow into next build. My favorite is overflow into a worker each time, though you *can* go settler>settler (would not recommend that without some experience)
Advantages are a very rapid 2nd settler time (40-50) which helps claim land and it can benefit very powerfully from traits like IND/CRE, and EXP to a lesser extent. It also lets you rapidly start gaining materiel (workers and settlers, units for fogbusting, even things like Granaries) in a short amount of overall time with BW's help. Disadvantages are it's even more map dependent and can be delayed even harder by your techs/lack of commerce to reach BW quickly. It also can trigger barbs faster, leaves your cities regrowing more instead of staying higher pop, can deplete forests you may want to save, and can crash your econ faster.
-Warrior first
-grow to 2
-Worker, continue on like the standard size 3 >slow settler example
In fringe cases where you cannot improve tiles right away even with an early worker due to seriously slow techs for the start, you may opt to do this instead while you are waiting on tech. A warrior is the most useful thing you can build immediately as it can fogbust, kill barbs if lucky, and if even luckier, maybe steal a worker from a close AI. Note that you don't build the warrior just to go take a worker (ESPECIALLY if you don't start with one!), you are doing it because you can't really use the worker right away anyway until tech catches up, and you are banking some growth in the meantime on the best build you have. Note that this is not optimal, because you are being forced into either 1) sit on a useless worker for several turns or 2) delay worker but grow a little -- because of a crappy starting tech/start location matchup.
-Worker first (15t)
-grow to 2, improve your 2 best tiles
-Settler slowbuild at size 2
A variation where you need to land-grab or have few good improvable tiles, and your tech sucks for the start -- you have tons of forest but are far from BW with little food/commerce, you have few uncovered hills and only one weak food, your only food is AH resources or several floodplains which takes forever to tech to/improve (I have had ALL of these happen to me before). The idea is to still get at least your first settler out quickly and find greener pastures, so to speak, while you let tech catch up so your worker can actually do more in the capitol. Note that just like the "grow to 2 first" example, this is not an optimal choice.
and one more just for fun
IMP leader
Settle with a 3H forest, or on a PH with a 2H forest
-Settler (17t)
-Worker in capitol (15t, or 12t with a PH settle)
-settler goes to new city location, and starts worker (15t, 12t if you settle on another PH)
-2 cities and 2 workers to improve them by ~35ish
It's very quick and another "I have to wait on my stupid techs" situation. IMP leaders have a 3rd option with the right tiles. Disadvantage is your tile development and growth will be slowed, which delays your 2nd settler/3rd city time (you have to spend turns growing!) but as you are now essentially developing two starting cities roughly in parallel, your 3rd and 4th settler times will be even faster. This can get extreme with strong tiles like PHMarble, or throwing in BW to the mix -- I've had 4 cities by T40 with Augustus before, and something similar with Vicky. It's a good way to get out of the "trapped" feeling of playing a poor start for Charlie too. IMP leaders are good fun.