75% of your problem is simply tuning the snare to the correct pitch so it doesn't pick up the bass so badly. I personally feel that if you are trying to record everything at the same time, guitars and drums, you'll never be happy because most songs cover enough of the sonic spectrum to make your snare go crazy regardless.
Get your drums in a room alone, and have a go there. A big part of the "natural" drum sound is bleeding between drums and bleeding between mikes. Your toms are SUPPOSED to make the snare buzz a little, your kick should make your floor toms ring a bit too. The extra ringing is what makes a really massive drum sound (because you can't do it with just one drum!).
It does not matter if you have 1 mic or 50 on the kit, snare buzz is an unavoidable part of recording drums, and it is actually expected. You remember that lovely phat, huge sound you heard on that favourite CD? Tons and tons of resonance in the snare, and that came with a lot of buzz, the buzz just got mixed out a little (because I bet they used 10 mics over the kit so they could afford to do it!).
1. Learn to tune.
2. Be realistic about what is achievable if you record everything in a small room at the same time.
3. Accept that some snare buzz is always going to be present.
4. Get a birch snare drum. Bye bye to most of your midrange interactions without touching a tuning key. They tend to better quality than a snare that you can't tell us what the model is to.