I vote for carpet. Not high loft, but a low tight weave.
I moved into the guest bedroom with my sewing almost 10 years ago. I've been rolling around on that bedroom rug all that time, and cannot see where I've been doing that. My chair came with my serger (the serger is suppose to be stored inside), and rolls easily over the carpet. The threads just stay where they fall until I feel like cleaning, and that is not every day.
When I tie quilts, the sewing room is much too small. I have to do it in the living room. There is a large Turkish area rug in there from 1954. While making the ties, I scoot around the quilt on my chair until I get to that rug. I sure is a pain to get stuck on that rug all the time. I have to get up and move the chair onto the rug each time I come to it.
So area rugs are not the answer. Maybe a vinyl mat, but I use nothing.