I'm just as happy running in a cotton t-shirt as a synthetic one, provided the shirt is close fitting. A loose cotton t-shirt, wet with sweat, is heavy and uncomfortable; a close fitting one is just fine. I don't find that I'm significantly cooler in the synthetic, moisture-wicking stuff, and I like the feel of cotton.
For winter, though, you need clothes to wick moisture (I like merino wool). And I`m not a believer in compression shorts, but people do seem to like the compression socks for running.