Hi i'm also trying to main adc this season and i'm feeling the struggle of being public enemy #1 always.
One absolute basic thing you need to do is to figure out what will get you killed in any particular game. Like if you're in a team fight you need to be aware of a blitz hook, a morg snare etc anything that will pretty much get you deleted if you get hit by it and position yourself accordingly.
Currently I've watched a lot of my replays and I actually found many of my deaths are because i'm not attack moving and one champion i'm trying to shoot suddenly retreats while another one walks foward and that half second my character goes to chase my initial target is enough of a mistep to get me killed, so that is one thing i'm going to be working on myself because i never bothered with attack move previously. That could be one thing you can work on also.
As for who to play just go for what you find fun, and possibly expand your champion pool as you go since many adcs can have similar playstyles and later on you can worry about who can fit with your team comp etc.
For example I like to play ashe when I have junglers with no cc like graves or nidalee, you can help them chase people or catch people with your ultimate.
or if you have a brand support he'll essentially just dish out extra damage instead of peeling for you, so it would be preferable to playing an independent adc like caitlyn instead of one that relies heavily on peel like kog'maw.
For general tips on climbing I highly recommend watching phylol, he makes videos daily now with updated information on solo queue, and he's also an adc main so a lot of specific advice will be about adc.
https://www.youtube.com/watch?v=EIX-psxrQXE