Finally silver. You can reach out of bronze too.
First of all, to reach out of bronze, you must be a great leader, you must communicate, don't be toxic, ping a lot, lead your team to victory, ward for your team even if it's not your job. If you're toxic and you get muted for 5 games, there's no way you can win those 5 games flawlessly.
67 wins, 59 loss, finally silver, mostly soloQ, i play rarely with friends.
Those are the champ i had to pick to win often. None of them are my main. From best pick to worse pick.

As
, i kept winning consistently; i often went on very long winning strict with him.
In my opinion, the best 3 champions to climb out of bronze.
is the best imo, but takes some knowledges, more than the others. With GP, you can win botlane when you didn't even waste your TP.
This is everything your champion need together.
AOE, AOE ult, AOE CC or very low cooldown CC, split pusher with a way to escape, get out of jail card: I.e GangPlank's W, Mundo's W or Quicksilver as part of your core build. Most importantly, always pick teleport if you're top and maybe mid too.
You need a fast wave clearer in order to fight with your team sooner if there's a team fight. Mobility will help you join the fight sooner too.
You need a champ who can constantly work throughout the entire team fight and initiate. To be a great leader, you need some type of initiation which also means that you need presence, ppl need to feel like you're always around even when you're across the map. This mean, don't pick 
order of Priorities:
1: ward Bronze players don't ward as often as they should. So it's your job to ward. Buy them, place them, don't upgrade your free ward because it's better to have 2 stack on you. Buy sight-stone if you must even if you're not a support.
1: Objectives. Towers and inhib only. Everything else is not important in bronze. A baron don't make your team win, it makes them become cocky. A bronze player will die for a dragon so once you get them in the dragon's lair, they will not back off when the enemies are coming. So forget about those unless your enemies are dead, but when your enemies are mostly dead, go for the towers instead, it's better to have map control in bronze, always better.
2: Defend your own objectives: Bronze players don't defend their towers. They often switch lane and they never come back. This is why you need TP and mobility. You must be everywhere: defend top tower, defend bot tower. You don't have to defend mid tower because bronze players like to play mid-war already. Again, check the dragon and baron only to trap the enemies, not to take it. It's not important in bronze unless you can take them without being contested at all. In fact, it's better to bait your enemies when you hide in the single bush. Wave clearing is good to push a lane and to not come back to that lane too soon in fear that an enemy might snipe your tower.
3: Team fight: If you're not about to destroy a tower and i mean, actually destroying it, not just damaging it, go join your team as fast as possible, don't let them die. Bronze players tend to be clumped-up, especially in the middle. You must be there to support their flaws and to save them or they will often die without you. Also, bronze players often fight in an unfavoured situation I.E: 3vs5, venturing in places where they have no vision only to get caught, chasing way too far, out of position, not fighting together even if they seem to be together. Bronze players don't hug towers, they stay away from them for some odd reasons and they often don't walk back toward the tower to be safe. A few AOE from you can easily make you win every single team fight, this is why it's so important. CC's will allow you to kill anyone who run or to save your team-mates from a killer.
4: save your teamates: Don't let your teamates die, go join him in his foolishness, slow down the enemy for him and get him back in position. You need everyone, so be a team player, not an individualist.
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List of champion that can consistently win bronze games in my opinion and based on their tools

for those who need a get out of jail card