Try Thompson tees (bamboo is best) there $30 a shirt and $20 shipping, they don't stop the sweat but they do a great job of wicking it away from your body and not to your outter layer. However are a bit of a pain to wash for they must be hung dry and never bleached and always washed in cold water.

I like wear 100% cotton.

Dark colours in meshy fabric or black cotton. Wool blends in lighter colours can be good if the fabric change when wet

3). Solumbra full spectrum UV protection (their expensive though!)
2). All cotton, unless I don't care.
1). Bamboo. It's soft, washable, moisture wicking and sustainable. Can be pricey, but it's a great textile!

I have tried all types of clothing and they are all the same for me. Al make me swear.