The title says it all. I need a shirt material that stretches. Is 100% cotton the way to go?
It is not so much the fiber of a fabric, but how it is made. Knit fabrics always stretch more than woven fabrics.
Supplex is my favorite stretchy material ever. Good luck finding a shirt made of it, though. If you do, you will love it. Supplex is the most comfortable stuff ever made.
What sort of shirt are you looking for? Since T-shirts generally are stretchy (some more than others), I assume you mean a dress shirt. Dress shirts are generally made of woven material, which limits stretch, and 100% cotton isn’t natually all that elastic. On the other hand, fella bilong missus flodnak has a polyester microfiber dress shirt that has a good bit of give to it. Don’t let the word “polyester” turn you off; now that textile manufacturers have really started experimenting with it, they have discovered fabrics that are both more comfortable and far better looking than the old double-knits and such.
I haven’t looked, but there may well also be stretch fabrics in shirt weight now - that is to say, shirts with elastic fibers mixed in, like stretch jeans. Knit dress shirts were fairly popular in the '70s, but you’re not likely to find them now because, well, they look like something that was fairly popular in the '70s.
The 70s? Anybody remember Qiana[sup]TM[/sup]?
/me looks in closet
most of my semi-strechy clothes are cotton + spandex blend.
Oh my, yes. I inherited a beautiful minty green Qiana blouse from someone when I was 11; that was my absolute favorite blouse for a long time.
The stretchier fabrics in my closet are also a cotton/spandex blend. They are quite comfy, but IMHO they’re stretchy because they’re meant to help highlight a woman’s curves. I don’t think men’s dress shirts are supposed to do the same. 
Men’s dress shirts are usually cotton or cotton/polyester blend, occasionally cotton/linen. (The cotton/poly blend is less prone to wrinkling.) The usual weave isn’t that different from a bed sheet, though, when you come right down to it - no stretch there, although oxford and twill shirts are “softer” weaves and may give you a little illusion of stretchiness. I haven’t yet seen cotton/spandex dress shirts for men.
Knit shirts (polo shirts/t-shirts) are typically some polyester/cotton blend, sometimes plain cotton (as with a jersey knit), but the knit does mean they have some give, as flodnak mentioned. Knit shirts also require a lot less ironing, if any (dry on low heat to avoid shrinkage, remove promptly from the dryer and hang on a hanger to finish drying before you fold them).
What do you need the shirt for - dressy? Casual but neat? Bumming around?