If you want to absorb sound with the floor, you want CARPET with a THICK PILE and a MAT.
If you think that putting something else down will have "sound-dampening" qualities, you're absolutely mistaken. Tile reflects sound. Concrete reflects sound. There does not exist some magical flat surface that somehow absorbs sound without talking half a million bucks per square foot because you're using nanotubes.
If you go with tile, great - it's much more hygenic than carpet. It's easier to maintain. But it's much louder and harder on the instruments - so you need to treat the WALLS and the SPACE to absorb the sound. Hang some acoustic treatment curtains across the room. Add some trapezoid/triangle tiles to the ceiling. Add ROOM TREATMENT not FLOOR treatment.
All that being said - if you DO choose carpet, guess what? It absorbs MOSTLY the MID and LOW range frequencies, and the high-range bounces off. This means your band will constantly be out of balance on a stage.
In other words - put the CLEANEST possible floor down that you can (I recommend that you use modular rubber tiles like in a weight room if you can - you can mop 'em and they have some sound-dampening qualities) and then TREAT THE SPACE. Carpet WILL NOT HELP unless you have a pad underneath and a thick pile!