Honestly I find the best way to pick a champion is to pick one not by 'gg this champ op' but by 'this is what fits the team comp'. I played Janna support a couple games ago because my Ashe adc was against a Vayne/Morg and she said she wasn't a good adc. Now I'm not a great Janna, but up against a heavy engage comp like Morg supp with a Lulu mid, that's what my team needed. We definitely won botlane both in kills and farm, and in teamfights it didn't matter that we were all half dead I built what my team needed (locket + crucible) and I chose a champion my team needed. I can't say 1/8/33 is a particularly good score, but KDA doesn't matter when you win the game.
It's nice to have a champion you can play well and not feed in every role, but it's even better if you go into champ select and not automatically say 'mid plz'. Instead just wait it out see what other people are calling and picking, go where you're needed, and play a champion that synergizes with your team (and screws the other team over).
If you can't get out of Silver 2 don't limit yourself to 3 champions, make sure you're adequate with a couple in every archetype and pick based on what helps the team.
Obviously you can look to the OP picks, Yas, Fizz, Braum, Morg, Jax, Yi, Blitz, Leona, Maokai, Akali are all banned a lot in Bronze/Silver, and they're banned because they do really well in those tiers, but when it's not you playing bad that's the problem, it's more than likely the team-comp that's letting you down.