Civilization – Which unit to build first

Typically your first build should either be a warrior/hunter, worker, or settler. Don't build buildings right away, the bonuses you get from them early on aren't enough to offset the slowdown in exploration and expansion.

While it might seem like you are slowing yourself down by building a worker or settler first, keep in mind that the city tile itself is always worked. So as soon as you have built two cities, you are working 4 tiles, at about the same time as your one city would've achieved this by growing to size 3. Fast forward to when both your cities grow to size 2, and you are working 6 tiles, much faster than if you had tried to let your city grow to 5. And the gains continue to amortize from there.

This is especially true if your initial city has a space with extra food/shields to build the first settler faster.

I have seen a devastating rush by the Mongolians under Kublai Khan:

• Keshiks are fast. You can not understand what "ignores terrain movement costs" really means until you have played with them.
• Aggressive helps with faster Barracks
• Creative helps get horses sooner, if they're close.
• Creative helps solidify your newly conquered territory surprisingly fast, with working the best squares, providing city defense, and keeping your troop supply costs down.

You should also look at anyone else with a fast ancient era unit:

• Persian Immortals
• Aztec Jaguars
• Egyptian War Chariots

Although winning in the first attack is ideal, fast units provide the option to setup a later win. Take workers, pillage improvements, hit the weaker cities behind the lines. In the ancient era Civs don't have the numbers of units to deal with harassing enemies, and small injuries like a lost worker affect the whole game.

Note: My info about specific civs is based on BtS. I can't recall anything being different in Warlords or vanilla, but I have not checked.