Need Help Climbing Out of Mid-High Silver into Gold

I'm having slight FPS and ping issues, but it's reasonably easy to deal with.

I'm a mid lane main who doesn't know what the easiest champions to climb out with are. I have trouble against assassins like Ahri, Fizz, Zed, Talon, Katarina, and Rengar. I just can't find champions that win lane against them by killing them.

I basically don't know what to improve on because everything just seems decent besides my kda, but that's because I'm against matchups where I just don't know what to do.