Your best bets are Mid, ADC, or Jungle. ADC is because they have the most damage output traditionally and can carry games with good decision making and proper positioning. They are reliant on a good laning phase though as they need the most expensive items in the game to have good dps. They are really squishy as well and usually the main target in a teamfight, so you might want a champion who can peel for him/herself if you can't rely on your allies.
Mid is great because they can be a high damage dealing carry that can destroy teamfights if they get fed. They have the most gold income and can hit items and levels faster than anyone on the map. As far as which champion you should choose; either get a snowbally bursty champion if you are aggressive or a control mage if you are more passive.
Jungle is similar to Mid in that they impact the other lanes, but for mid this objective is kind of a sidequest whereas one of the jungler's main jobs is to impact other lanes. They also are very important in objective control as they help take towers all over the map, can access the teamwide buffs of Baron and Drag, and can do a lot for vision; (though for Bronze; people tend to forget they have a minimap sometimes). I recommend the tank junglers, particularly those with hard engage to carry bronze; DON'T play Lee Sin, unless you just want to have fun (which you should play normals) or you have put a LOT of time in with him and are more confident in him than your other options.
Why Top and Support are not great for solo queue carrying: Top lane has the least amount of impact in the game. Yes they can roam, yes they can TP into a fight, but they are mostly farming and/or dominating their lane opponent at most times so they can be relevant in the later teamfights after towers are taken; or they take the role of split-pushing: which is going to become easier in the next patch so look out for 
. Top laners are usually not hard carrying champions as midlaners or ADC's are, but they offer something that will benefit their team comp and that is why it is the most diverse lane.
Support is probably more impactful than top lane, but they lack the damage and/or tankiness to be as strong as other roles. Supports CAN carry, but it's hard for them to do so in a more unorganized environment, because they lack a lot of combat ability when shit goes wrong. They can do a lot of roaming to impact the other lanes, and they can do a lot for vision like junglers, but they have the lowest income in the game and support champions usually have to buy items that are better for their team than for themself. Lastly, being a support in bronze is a nightmare, as your ADC is going to flame you if they die and everyone is going to wonder why you haven't warded the entire map even though you are the only one who buys any wards.
Good luck out there. Peace.
is pretty good, they will either have to babysit you to deny you Q stacks or watch as you destroy them.
Any that can carry hard, like 
etc.
A big part is counterpicking, don't lock in a champion without giving it any thought, and don't pick a counter just because it's a counter if you can't play the champ.
From one Bronzie trying to climb to another, good luck!
. She seems like a solid pick for climbing, and I'd like to expand my mid lane role, or I could even add her to top lane. Just browsing guides and videos of champions you're interested in can help you so much.
