How new is your construction? If brand new, settling has not finished and you have not been through seasons to be certain your basement is dry.

Personally, I do not propose carpet in any basement unless it is a walk-out. Even then there a possibility of leaks from the foundation, and sump pumps do fail (even with a back-up) and water heaters eventually leak. I even once had the discharge tube from my humidifier clog thanks to some insect!

So, I recommend tile and area rugs. Ceramic, of course is the top-of-the-line choice, but those too may crack as the basement floor settles. In ours, I installed 12" vinyl but used tile adhesive, not stick-down ones because there are slight variations in the concrete which the stick-downs don't form to very well.

Another option which can look really nice is stained concrete. Hope this helps. Good luck.

Check out DRICore flooring product.
I put it down in basement apartment.
I have both carpet and vinyl tiles installed on it.
I like it very much.
It takes away the slab floor feel. It is warm in winter.
It gives some protection to moisture from below.
It is kind of expensive $1.25 per square foot (approx)
It is easy to install, and well made.
Home Depot carries it.

Good luck
Carguy

I've used synthetic carpet direct-glued in basements for many years without problem. I'd definitely avoid underpad though, as it tends to absorb the water vapour that's passing through it. I've also used ceramic and natural stone--slate, granite and marble. Their main drawback is that they're cold to the touch.

The universal problem I've found with basements is how many owners are convinced they don't need a dehumidifier because they have central a/c, or that their basement is "dry."