Already lots of good answers on here. I'll just reiterate and give my 2 cents. :)
We used prefolds, Bum Genius, GroBaby, Fuzzibuns, and Thirsties. We had occasional leaks out of the sides, but it would only be like a tiny smudge. I think some of it depends on your baby's shape. Ours had super chunky thighs, so I was always worried about covers and such being too tight around her legs.
With the prefolds, are you just laying it in the cover or are you actually folding it? Make sure you're doing that "extra" pocket type fold around the legs and at the front/back.
Also, good suggestions on checking your detergent and stripping the diaper if needed.
There are also a lot of "try and buy" packs out there if you're worried about "wasting" money. They send you new diapers to try (variety of brands) to see what works best for you and your kiddo.
HTH!