So, I've gained about 250 Elo the last two weeks, which is quite a lot. I mainly did it with AP Yi (see here), however, I started playing him a bit less, mostly because I didn't feel like all the flame in champion select wasn't really worth it anymore, and because I slowly got enough of a team that didn't initiate every third game, thus rendering me useless and making me unable to carry. I have also played a bit of Morgana and Katarina lately, but again, I can't carry. With Morgana not because the initiation must be followed and we must survive the early game, and with Katarina not because I'm just not good enough with her.

Now, does anyone know a champion that, once mastered, can carry in nearly every scenario? Of course, it's solo queue, there's always the chance that your team is just too bad, but are there champions that can also initiate and win team fight, and deal the damage if the team lacks it, and have a strong influence early or just strong game early? (note here that I am not really good at junglers, as I am bad at counterjungling and don't always see when I can/should gank, not to mention that I for some reason just can't play some junglers, as if a coin is flipped for every jungler)

Also please don't come with "omg you don't know all the champions"-type of answer, yes, I know all the champions, but sometimes I don't know what they can do exactly.

PS If I say something along the lines of "I can't play the champ you suggested", then please let it be clear I still appreciate your help. Any answer that makes sense is useful for me.

EDIT: I was also hoping that others could be able to use this too to find someone who worked well in rising Elo. Forgot to say that.