What champs are the best for mid-late game?

Good teamfighters are insane late game. I can personally recommend Amumu and Sejuani for their ults, general tankiness, and moderate damage. (Sej being a lot more cc based, and amumu having really high late game damage)

Im no expert in fact im bronze haha but here are the champs i think Nasus vayne Sejuani ziggs

go ahead, GO AHEAD and just TRY to duel late game Jax

Rengar, but you have to take time to learn his fairly fast combos and find clever ways of dealing with his awful early game.

mainly sated devourer champions or super tanks

kha can be good too if the enemies dont group much