There is no best role or champion which can carry you out of Bronze. Carrying yourself out of bronze will require reflection on your strengths and weaknesses and then figuring out which champions and roles work for you. About a year ago i replied to a similar post asking the same thing and i will tell you what I told him: [small edits for your specific circumstances]
A lot of other people will tell to master champions but that advise is not that good. Its equivalent to "be good at a champion". And well yes, if you're good at a champion you will win more games than if you're not good the platitude neither tells explains why its happening or tells you how to get there.
Anyway a bit about me so you know where I am coming from. In Season 2, I ended up at 1450 ELO (about silver 1 today), 50 MMR short of rewards (So no Vicotrious Janna for me :( ). In Season 3 i meandered around roughly doing the same thing until I came upon some really good advise. In 2 months i went from silver 1 to plat 3 and have hovered around there ever sense.
Specifically this advise was
1) Stop playing when you lose
It instills bad habits in your play. Repetition is memory and you play like you practice. If you repeat bad habits in your games you are practicing bad habits. Tiger woods had the same comment on bad golfers. He said (unspecifically) "you can tell a bad golfer by the way they repeat their swings after they shank one, good golfers forget bad swings"
We want to forget our bad habits. This is regardless of how well you played. Because of the second aspect of losing games.
Losing games makes you negative. Negativity begets negativity. You just lost a game, maybe it was your fault maybe it wasn't. Now you're unhappy and you take that out on others. Maybe intentionally, maybe not. That makes them unhappy. They play bad. You lose more. We call this "going on tilt". And its a real thing. The key to avoid playing on tilt is not to be able to realize you're on tilt and stop playing. Its to stop playing before you go on tilt.
You cannot downplay the importance of this. If you're unhappy because of the last game you will be less likely to trust your teammates. If you can't trust your team mates you will, by your inaction, turn their good plays into bad play. If you turn their good plays into bad you will not think this was your fault and you will get more negative and even less trusting. Which unsurprisingly leads to even worse play.
If you can definitely not do this, or you're a professional and you have to play that next game, then go right ahead and queue up. But for most people they cannot help themselves, they do not realize they're doing it, and the only obligation they have to play another game is themselves.
2) Analyze Every Game
One day later sit down and look at all the games you played. Watch replays if you can get them(Riot please, for god sakes finish this). Turn enemy vision off. Ignore your teammates play and focus only on yours.
The goal of this session is to find 10 mistakes that you made in each game. "Missing a CS" does.not.count. These mistakes can be mechanical (missed my combo, failed my flash, right clicked instead of attack moving), strategic (built the wrong item, was in the wrong position on the map, got picked, didn't ward, didn't buy pots, leveled the wrong ability), or tactical (went into a fight i should have been running out of, didn't flash an ability i should have flashed, put a skill shot in the wrong direction, was in the wrong position in a team fight). But you should find at least 10. That doesn't mean you should stop at 10. Find as many as you possibly can. The next time you play focus on not making those mistakes.
If you can't find 10 you're wrong. Look harder. If you still can't find 10 then you can't get any better. So go find someone who is better than you and ask them to find 10. They will find 10 easily. If they can't find 10 then you've peaked. You haven't peaked. God find 10 more mistakes.
The purpose of this is to do two things a) get you to focus on your game and your game only. Especially while you're playing. And b) to make sure you don't make those mistakes anymore.
3) dedicate time to practicing champions and farming
I am apparently out of space and will continue this by replying to myself