I'll assume you like getting into peoples face's and going BOOM **** load of damage. Then I would recommend Jax, Lee Sin, maybe Wukong.
These three heroes are melee burst bascially, you get in their faces, do a bunch of damage, with a little bit of auto attack supplementation. I'll also assume you don't love graves because he can auto attack lots, but if that is the case do tell. Someone whom may differ a little from your tastes is Vladimir.
He's a mage, but can build a good amount of health, allowing for a burst damage person, that has the option of getting into someone's face. Also, once you kind of get out of you champion hopping stages, and have established who you wanna get better with, just keep playing that one guy for like 5 -10 games in a row (not in a single day lol). Anything you DON'T smooth out after that series of games, would then we probably what you want to consult other people about.