well I like to play all civs, so my favorite civ is Random. My ratings of the civs will be tiered because some are just plain equal IMO. This is assuming you are playing some vanilla water type map, continental, coastal, mediternaean or narrows, since these are most common. Its also assuming ROR, not AOE.
Tier 1- Shang, Phoenician... yes I think phoenician are almost as good as shang in ROR.
Tier 2 - Minoan, Hittite, Sumerian, Egyptian.
I hate putting minoan in the 2nd tier but the ships are just too powerful If you don't agree with sumerian being tier 2, you've never seen an expert TC boom, did a 70 villager + 30 boat iron in 28 minutes with them with a 14 minute bronze and built an army with them the other day fooling around against the computer. Had all super upgrades by 40 minutes.Tier 3 - Rome, Assy, Yamato These civs all kinda suck, but they have an economic advantage early and that will win games. Rome is more like 2.5, they are good in iron at least, assy blows in iron now, and yamato always sucked in iron IMO.
Tier 4 - Babylon, Choson, Mace - these civs are just average all around, though if you can get legions and still control some gold Choson kicks butt.
Tier 5 - Greek, Persia, Carthage, Palmyran - if you win with these civs vs someone good feel good about yourself.