You have a lot of options - My opinion these are the three best:
Tile floor - best heat transfer. Put an isolation membrane in and you won't have to worry about cracks in the slab projecting through. Not great for acoustics and no matter what tile you pick one day it will be outdated.
Luxury Vinyl Tile (LVT) - floating floor, thin and a pretty good heat conductor. Goes in easy, not bad acoustics but not as good as carpet. Easy to change 15 years down the road, easy to clean
Thin Carpet (glue down, no pad) Best acoustics, easier to stand on (think game room/movie theater/casino). A little more money for the gameroom themed but looks good. A little harder to change out (scrap up the old glue) but easier than tile.
I would say:
1. LVT first - the higher quality have built in acoustic material, along with waterproofing (good for a basement). Self install, super easy
2. Movie/Game Room or commercial patterns, glue down, thin carpet themed or patterned (professional installation, especially for seams)
3. Tile floor with an isolation membrane - worst acoustics but DYI install (unless using the very big 24X24 or bigger tiles, these can get tricky without experience