To start with I suggest focusing on one champion, but don't be afraid to experiment with others and new item builds.

If you are sticking with just one, read up on the rest of the champions and their abilities so you know what you face and what items you need to choose. As you learn your chosen champion, you can learn how to build and play differently to counter your opponents. This will keep you in good stead even if you want to swap champions later.

Imo you should alternate between 2 champions, if only for the case someone else picks your champion.

I like playing with a pretty big pool of champions. By becoming familiar with multiple champions you won't get your Elo stuck real high or low because the one guy you picked is over/under-powered. You won't get stuck in a fixed mindset for items and ability rotations. Lastly, knowing how to play a champion really helps when you face off against that champion--you know how the abilities work, what to watch out for, and how to counter certain effects.