I can't respond to your question on my Youtube video for the circle skirt tutorial- it has something to do with your Google+ settings. But I thought I'd post a response here for you.
Any spandex knit fabric should work. If you want the feel of a t-shirt, you want cotton/spandex. Online, you could search for "cotton spandex knit" or "cotton lycra knit". Joann Fabrics carries a cotton/spandex rib knit that is a nice quality, and I think it's what I'm using in the video. I believe it's a 95% cotton / 5% spandex, so it doesn't have to be all spandex.
Just make sure you're buying a knit fabric (like you'd find on a bathing suit or a t-shirt). There are some spandex blend woven fabrics, and they would NOT work.