So it seems that a lot of people face a similar problem that tends to hold them back when it comes to League of Legends. I see this a lot in the team I play with and I have experienced it myself until here recently. It is the inability to pick a champion and stick with them.
LoL offers many champions, and they are constantly adding to the number. To many people playing the game, it is hard to pick one and stick to them. This holds you back, for obvious and less obvious reasons.
The biggest screaming reason you should pick a champion and maybe a backup in case your main gets taken is skill. Until you play a single champion main, you are not going to build up the skill with that Champion to be any good, especially if you are trying to climb ranks and escape ELO hell. Only practice is going to give you that skill and you are not going to get that my switching champions every match.
The other major point is optimization. Each champion has a different set of runes and a different mastery setup to optimize that champion to be the best they can. There is no easy way to pick a champion to play than to try them out till you find one you like, but once you do, stick with them, get better. Check out MOBAFire, they have lots of guides for each champion to assist you with how to play that champion, written by people that play the game a lot more than me, and odds are, more than anyone reading this.