If you like to wear T shirts as a base layer, I would look at On One's merino T's. They are pretty cheap and will wick moisture much better that a cotton T.
I appreciate that sneaking a few miles in during a working day, you can't get all technical with riding gear, but as someone who wore cotton T shirts for years, back in the 80's and 90's, they really do have the wicking properties of a dish rag.
I never wear cotton ones, you can get good ones for not a lot of cash from outdoor shops. I got a load of cheap Regatta tech material ones last summer at a fiver a pop, good wicking and dry out almost as soon as they are damp. Obviously not as good as merino but decidedly better than cotton ones.
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