
All of these champions fit that description.
Aatrox is the very definition of sustain in this game currently. His Q can be used as a great escape and has an opener to a team fight while his E can also be used to disrupt the enemy team and poke with a heavy slow. He isn't super easy to play, but isnt extremely hard either. Top and Jungle
Gragas has sustain through his passive, the weakest of sustain here. However, he has pretty good escape potential and arguably the most presence in a team fight of everyone listed here. Like Aatrox, not super easy, not super hard. Need to learn how to manage where the enemy is with his ultimate. Top, Middle (arguably), and Jungle
Shen has been listed here many times, but I will list him anyways. His sustain has been known for making him an absolute brick wall in lane that is extremely hard to get out. His E is a very good escape AND makes his presence in a teamfight huge. His ultimate is also incredible. He is probably the hardest of everyone listed here, almost entirely due to his ultimate, but you can give him a try. Top, Jungle (arguably), and Support
Zac fits everything you said to the extreme and probably fits this more than Shen, actually. His sustain is insane and his escape potential through his E, although limited by hard crowd control (who isnt?) is almost the greatest in the game. His E and R make him an INCREDIBLE initiator in a fight and his passive size increase from health makes him a great meat shield for the first bit of the fight. On a side note, his deceivingly good at dueling and most wont expect that. Just pick up the blobs. Top and Jungle
If I were to recommend one of these, it would DEFINITELY be Zac since he fits all of your wishes to the extreme while everyone else has something else strapped onto their kit besides your wishes. Zac is the living and breathing combination of your "looking for" list.
TL;DR I would heavily recommend trying
, not only because he fits everything, but because Aatrox and Shen are planned for reworks and Gragas has the weakest sustain of the lot, which I think is what you want the most since you listed it first and at the top.