Congrats on joining the bass community and deciding to be a bass player.
I don't know whether your bass is set up properly or not, but the set up and strings ringing are, IMO, two different and unrelated things.
The best thing to fix the open strings ringing is really boiled down to technique. Both your fretting hand and your plucking hand should share the responsibility of muting the open strings and to keep them from vibrating.
I think this guy has great technique, ability, sound and control:
http://www.youtube.com/watch?v=CyTQzA8_kI8
Grab your bass and mimic this fretting hand position, keeping in mind that it's totally fine for your pointer finger to touch the A, D, and G strings when you are playing something on the E string. This is one example of the fretting hand providing muting the the other three strings.
Even though it's a tough song, and it moves quickly, I think it's a good example, as the bass part runs across ALL the strings, and there is no extraneous string ringing, and the bass notes are stacatto and controled. There are probably more simplified (and slower!) examples around, but I always come back to this one.
I'm sure there are folks who who are better wordsmiths, and may better be able to describe this muting process than I can, but I think it's a concept that's tough to put into words, in general.