Cotton ON to this line from Under Armour.
Cotton t-shirts are well-loved but they are not great for tennis. Once a sweat sets in they get wet, stay wet and cling. Under Armour's line of performance cotton (UA Charged Cotton) which weaves hydrophobic and hydrophilic fibers together, solves the problem.
Same soft, smooth feel as as old-friend tee, the new line really does wick and dry fast. I like them for the gym too. Basic tee for a guy but select women's tops have a loose but close fitted athletic cut (look for the words "semi fitted" on the label). Nice coverage up top and they are long, keeping that less-than-perfect zone under wraps while serving.
If you have been steering clear of cotton, check this line out which includes crew and v neck tees as well as shorts. Both tops pictured run $24.99 USD.
Find the line at Under Armour, Tennis Warehouse and tennis retailers worldwide.