League of Legends (LoL) Question: With what champion should i use?

It is virtually impossible NOT to die in a game (unless the enemy team is so bad, it won't even matter). Sometimes, you will have to die in order for your team to get a lead, sometimes you have to die because of a bad move you made.

If you don't want to die, the only advice I can give you is to learn how to play better.

You can't have a champion that not die, actually, but if you like someone that don't die much, pick a tank top, like : Garen (Passive regenerates health !), Tryndamere (His Q steals life, if I remember) and another tank champions. For these champions, do full tank/health regen/life steal (depending on the match).
Tips for not dying :
1- Play behind the minions, farm safe.
2- Be alert of possible ganks, for this I would recomend flash.
3- Don't take risks : is there a champion at the tower with low health ? Don't go for it, take out the minion wave, and when you get to the tower, deal the maximum damage at him (If you can't kill, don't risk yourself, get back to the tower).
4- Return to base. Let your health regenerate, return to base when you are with low health.

I hope I have helped.