Acoustics is a deep subject, but here is a pretty good primer: http://ethanwiner.com/acoustics.html
That said, a simple and excellent solution is to make absorption panels yourself. Make a frame from 1x4 inch wooden boards (fir, plywood, whatever). Cut a 4 inch sheet of mineralwool to fit inside the frame (or dimension the frame to take a whole sheet), finally staple an old cotton bed-sheet or similar to the back and front of the frame - and you're done. The cloth keeps the dust inside the frame.
Mineralwool is usually rated as fireproof, so you're good there.
I have several of these in my small home studio and they work wonders.Place them directly on the wall for mostly high-freq damping, or put some space between them and the wall to damp mids and lower mids. Putting them diagonally across corners between walls/ceiling, wall/wall, or wall/floor is a good idea also - if you have the space.
Read more in that link above, or google "diy acoustic treatment".
Build a few of these and save some money for more gear!