checkout shirtspace, or any site that lets you order shirts to print on. They're usually a few dollars each and you can get them in bulk in different colors. Different fabrics, styles, weights, etc. Literally shopping for tshirts by specs instead of look.

Tshirtwholesaler, try a few different shirt brands and styles out. There's so many that are plain white (or color) tees, only potential branding is against your neck on the inside of the shirt. I actually dontind having something there, because sometimes someone's like "Hey, what kind of shirt is that, it's soft, I like the cut, it wears nice," and then I direct them to the tag or print at the inside collar for information.

Hmmmm, sounds like advertising....

Bronson Mfg has some good solid shirts that are 100% cotton.