This is what I do. I let the game choose who I am going to be and then I try to play to the strengths of whoever I get. I enjoy this because there are SO many choices -- if I have to pick for myself I either get choice paralysis or fall into a rut of always playing the same three or four ones.
Lately I've started messing about with mods (using other people's mods, not making my own). I'm not looking for gigantic changes to gameplay but I'm excited to try the Steel & Thunder mods that add more units, and the Real Tech Tree mod that adds more dependencies to the tech and civic trees. I also added a couple of Sukritact's civs/leaders -- they are incredibly well polished and look just like official Firaxis DLC.