Good adc for me!

Hello, I've been wanting to get into adc for a while, but I don't know what adc to get. I want a champion that has a good early game and good late game. That can carry teams and do alot of damage if they are fed. I've tried alot of champions but they all had problems. Varus is to weak late, vayne is to weak early, sivir does no damage. Here is a list of all the adc's I've tried: Ashe, Vayne, Jinx, Varus., Caitlyn, Sivir. Out of all those champs, the one I really liked was jinx. The problem was jinx has no escape. I was wondering for your thoughts on what adc I should buy? Should I still buy jinx or should I consider a different champion? Srry about my english.

btw this is not my main. My main is level 30.