My only question is how you have barely any champs as a level 29, and how you have barely enough champs to play draft.
Anyways, you want to play carry champs.
List of carry champs:
Kindred - 6300 IP - Jungle/Mid/Top - Medium - Strong carry, needs small amount of team support.
Ekko - 6300 IP - Jungle/Mid/Top - Medium - Weakish carry, relies on using lead to help team.
Kalista - 6300 IP - ADC - Hard - Strong carry, very powerful in teamfights. If strong enough could 1v5 depending on circumstances
Yasuo - 6300 IP - Mid/Top - Hard - Becomes irrelevant late mid game, strong early game. Should use lead to help teammates.
Jinx - 6300 IP - ADC - Easy - Strong carry entire game, just needs a support and a tanky frontline.
Zed - 6300 IP - Mid/Top - Hard - If fed basically gets his choice in type of kill, needs to use lead to roam.
Rengar - 6300 IP - Jungle/Top - Hard - Great carry, but as he's a jungler getting fed means more for the lanes.
Diana - 6300 IP - Jungle/Mid/Top - Medium - Strong all game, preferred that she uses her lead to get atleast one teammate ahead as she can be easily shut down.
Draven - 6300 IP - ADC - Hard - Strong carry, strong 1v5 potential. Late game chance to oneshot enemies. (with a q auto)
Darius - 6300 IP - Top - Easy(?) - Unkillable frontline, strong carry, can almost 1 shot anything cause of true dmg ult. (Play to carry in teamfights)
Ahri - 4800 IP - Mid - Easy - Strong early to mid game, semi falls off late game. Use kills for roams.
Fizz - 4800 IP - Mid - Easy(?) Strong early all through late, preferred roam but possible to snowball lane hard enough to just carry team alone.
Graves - 4800 IP - Jungle/Top/ADC - Medium - Carries teamfights, strong all game.
Vayne - 4800 IP - ADC - Medium - Carries teamfights, solo carry, strong pick potential (as well as tank killing)
Riven - 4800 IP - Top - Hard - Difficult (high risk high reward) strong early mid to late game, cannot carry a team alone.
Brand - 4800 IP - Mid - Easy - Strong all game, can carry a team in teamfights and also has strong pick potential and good seige.
Caitlyn - 4800 IP - ADC - Easy - Good starting adc (with long range) can choose to farm to late and be a monster or get kills early and try and snowball game.
Leblanc - 3150 IP - Mid - Medium - Strong all game, needs to roam to carry team.
Kassadin - 3150 IP - Mid - Hard - Team carry, potential 1v5 with strong pick potential.
Gangplank - 3150 IP - Top - Medium - Teamfight carry, weak single target lock down but can chunk adc's.
Karthus - 3150 IP - Mid - Hard - Late game monster no matter (unless you feed) with potential 1v5 (gotta land those Qs)
Twitch - 3150 IP - ADC - Hard - Weak early game, strongest late game adc with very high pick potential. 1v5 is not super hard.
Katarina - 3150 IP - Mid - Easy - Strong teamfight carry (3k magic dmg to 3 enemies each?! Awesome!) can snowball lane, good pick potential.
Mordekaiser - 3150 IP - Top/ADC - Medium(?) - I don't know much about mordekaiser, though I know enough to say that he can carry a game if he gets someone else fed.
Akali - 3150 IP - Jungle/Mid/Top - Medium - 1v5 potential, strong all game/very hard carry.
Heimerdinger - 3150 IP - Mid/Top - Easy - Good teamfight/disengage and can easily win lane (with semi high chance to get fed)
Miss Fortune - 3150 IP - ADC - Medium - Late game monster, good teamfight. Relies on good peel to get ult dmg out.
Tryndamere - 1350 IP - Top/Jungle - Easy - Potential 1v5, can carry entire team by himself.
Jax - 1350 IP - Top/Jungle - Easy - Potential to snowball game. Semi-good teamfight.
Tristana - 1350 IP (or free if you follow/like their facebook) - ADC - Medium - Strong pick potential with huge teamfight strength (and pushing power, along with jinx)
Master Yi - 450 IP - Jungle - Easy - Can snowball game, 1v5 potential. Hard to solo carry game with.
For those who are gonna say they can play other roles I'm stating roles you can carry in.
Also, I know I wasn't super consistent with my descriptions but I'm tired. Goodnight.
[slayer-jinx-wink]
And yes, I made this at 5:40 in the morning, cause I have nothing better to do.