I've written a number of posts on winter gear, such as this one on layering and this one on wool shirts and this on shoes. Now that we've officially moved into summer weather (regularly above 80 F) in the northeastern US, I thought I'd address the Great T-Shirt Debate: natural (cotton) or un-natural (polyester)?
Polyester/rayon/nylon/whatever blends are generally cooler and lighter. They also dry out well. However, they don't wash well: any dirt gets pretty much ground in there permanently, and mine smell distinctly of sunscreen (and probably sweat, although the sunscreen is most noticeable) even after being washed multiple times. Also, they don't hide anything underneath, and I have to wear a distinctly, ah, supportive and thick sports bra in order to not be indecent in them, which kind of negates the "cool" part.
Cotton t-shirts tend to be heavier. They don't dry out all that well,
and will stay damp for ages if you've been sweating in them. However, they're also safer if you (or a contractor you're overseeing) are doing any welding, grinding, or other hot work, because sparks that land on them may smolder and scorch them, but won't melt them to your flesh.
So what do I go with? It depends on the weather. If it's going to be brutally hot out or I know it's going to rain the whole day, I'll go with non-cotton t-shirts. If there's a chance for passing showers or I want to give the serious sports bra a rest, I'll go with cotton to prevent any issues with the shirt becoming see-through. I also think that cotton layers better, with minimal static if you have to peel something off. So when I'm in the field, I bring a few of each.
I think most of the contractors I've worked with are all-cotton, but that may be because cotton t-shirts are cheaper and are more permanently silk-screened with the appropriate company logo. If you do a lot of fieldwork, do you have a preference for one or the other?