I haven't been playing the vanilla game for long, & three I have found that suit my playstyles are in no particular order.
Alexander (Greece) - Can be good in a dominating game with their Hoplites & Companion Cavalry early on & also have great advantages when dealing with City-States, which can build up your cities & help with a diplomatic victory.
Elizabeth ( England) is good if you play on islands (archipelagos) with her Ship of the Lines & increased naval movement. Also their longbows can be very effective as can fire three squares away, & have to wait until artillery for any other unit to do that.
Ram (Siam) - I found these highly effective & always a nuisance if one of the other civilisations in your game. Have a good elephant unit, & an update on universities (Wat). Leader also gains +50% resources gained from city states you have allied or friendly with. The increased food alone can really build up your cites & don't have to concentrate building farms so much.
These are my favourites so far, but I expect others who are more experienced may know of other ones that are superior.