The trick now-a-days is making sure your basic tee shirts are made out with 50% cotton, 50% polyester.
100% cotton will not hold up well for a long time. It's all natural which means it's not perfect. Other man-made blends of fabric allow them to be made "perfect".
The best places in my opinion to find shirts and other articles are American Apparel and Urban Outfitters. Multi-blended shirts are not exclusive to these stores, but they do do a good job with it.