Stay away from tile. If the cue ball flies off the table and bounces on the floor you will most likely crack the tile. I would stick with wood or carpet. Carpet would be the best due to pricing and sound insulation.
Here's a photo of an install we did where the customer wanted wood but decided to have carpet installed under the pool table with wood around it. This way if a ball did fly off the table it has less of a chance to damage the wood.

Carpet · More Info

Hardwood · More Info

We are not a fan of an area underneath, as it often doesn't look the greatest. If you do decide on an area rug, be sure to get a big enough rug so that both feet are on even ground.

The balls should not be flying off the table on a professional made table for the home. If they are flying off the table, you are shooting too aggressively. This is a game of finesse, not how hard you can smash the balls around.

Tile that looks like wood looks amazing!!!!

Or even a nice floating laminate floor. The pool table will not be directly on the floor, we must place very thin rubber pads (invisible) underneath the legs to prevent anyone from trying to push or slide the table. They are very heavy, but we have seen many things over the years.

Please let us know if you would like to discuss further. Best of luck with your project.

James G

I would use a hardwood floor under the pool table.

Pool is noisy. Adding more hard surfac s makes it echo even worse. You need carpet. And you need other soft furnishings to absorb sound.

Another good option is cork.

http://www.torlys.com/residential/products/cork/

While carpet is an option, if you want a hard-surface product that can handle the abuse of a pool ball better than hardwood, consider vinyl plank. A high-end vinyl plank will be considerably more durable than hardwood, and more cost-effective. Take a look at Modin Vinyl Plank, which has the most durable wear-layer on the market (40 mil):

Noret Vinyl Plank · More Info

Barin Vinyl Plank · More Info

Cork works very well...balls bounce but don't do any damage and are not very loud.