I love the Ottomans for conquest. Played right, the UU can be the dominate unit for a long, long time and it is good at busting rifles and even infantry under conditions. And with scientific/industrius traits, you could do a lot worse. I only have PTW, so for me, industrious is the best trait (IMO). That only works if you plan for the game to last long enough for the UU - larger maps.
I actually like Rome for AA units. A sword and a pike rolled into one, but they are slow. But well placed legions makes most of the AI units dance round wondering what to do. They don't want to attack those legions on the hill/mountain, but they need to get to your cities . . . What to do. And Militaristic/Commerical makes them competative even without industrous workers.
All of the other suggestions are, of course, equally good (or better).