If you have the original bridge, low E will probly be your biggest problem.
ie: string comes out of the saddle/adjustment screws come loose the most etc.
check out the boards theirs lots of posts about ways to fix these things, but any other Q's just ask if ya can't find em.
As for the strings touching the back of the bridge I don't think they should do that, maybe your bridge is a little high, my MIA jazzy just barley touches, maybe lower the whole bridge then raise individual saddles.
