When I bought this house I had all the carpet replaced with Pergo, a laminate. I have a number of area rugs, but the sewing/quilting room is all laminate, and I really like it that way. It's easier to find pins, easier to clean. But it doesn't get really cold here, and you need to factor that into your decision.
I had a basement at one time, and it had moisture problems. Carpet down there was NOT a good idea. When it got damp it smelled of mildew - had to rip it out. Hopefully your basement is better sealed than mine was.