Just about every running/fitness/hiking/athletic brand makes lightweight tech t-shirts: Nike, addidas, UA, Marmot, Patagonia, Brooks, New Balance, and on and on and on. In the US, the cheapest place to find them is Marshalls or TJMaxx. They always have several options in the $15 to $20 range. I've got three long sleeve Marmot Power Dry shirts that I got there for $16 each.
They all make very thin warm weather base layer options, often with breathable mesh. The Patagonia Capilene 1 shirts are paper thin.
If you want Marmot, any of these short sleeve shirts would be fine:
The main thing to look for is fit. Some are looser fitting. Some are tight and stretchy.