Mid

Top

Jungle
or 
Support

ADC

This is what I generally see from my games and from watching my friends climb to high Silver from Bronze 5. The biggest thing that helps so much is becoming a one trick pony. Pick a champion you're good with, learn to play them well, then pick 2 or 3 backup champions. The people stuck in Bronze usually play upwards of 6 or 7 champions. They're decent players like those I see in Silver, but they can't stick to a small rotation.
Gold is still considered low ELO, and that's quite a difficult league to pass through if you're coming from Bronze or Silver, but if you're looking to get into Gold or high Silver, those champions are strong meta picks that can help boost you up. Of course each patch is different, but I'd argue that most of the champions I listed have remained top or viable picks throughout this season.
Another tip is if you find yourself slowing down, it's not because of your teammates. You're just learning and there's nothing wrong with that. You have to trust that if you're meant to move up, you will. Everybody has bad games, or games where they did the most on their team and still lost.