It depends on the sound you want.
I find it easier to get a drum to make a tone that "fills" the room when it's on a shiny floor.
BUT
When it's on the shiny floor I have to attach the kit down... I've tried everything, I settled on screwing the pedals to a piece of particle board and dyna bolting that to the concrete. the kick drum sat on a small piece of the same thickness board to bring it up flush and the snare was wired to the pedal board. Like a mini drum riser on concrete.

Playing on concrete vs carpet is a totally different ball game logistically and sonicly(is this a made up word?).

On concrete you get heaps more high end, defining amounts of treble. This can be a good thing. Depends on what kind of sound you are after.

You could describe it as brighter with a lot of attack.

I have a pretty budget studio with Dricore for the floors, wood walls with blankets stapled to them. So as you might have guessed I also deal in budget solutions for the drums sliding around in which case I find duck tape works well. It's a little tricky to get it around the base of some of the legs but if you can get it nice a tight that drum kit stays put. Also I don't know enough about room acoustics to know exactly what my room creates, aside from cutting down on some re-verb.

Depends on what your ceiling is like, if it is low and untreated I would say use a rug.

Sand bags used for the backs of pick ups and such work wonders for holding drums in place.