I have a half-dozen pair of very old-fashioned long drawers, summer weight. I think they're Czech, probably about 40 years old. They're woven, not knit and have a drawstring waist. They're rather like pajamas. I like them for wear under thin summer-weight trousers inside and out. But when the weather turns freezing, which is will in another month or less, I have the long johns I was issued when I joined the army in 1965 and they're pretty much sufficient for winter here. But I have a thicker, more recent army issue pair, too, that I also use. Cotton is perfectly fine for the bottom because your legs won't perspire like your upper half.
For the upper half, however, wool is probably good enough. I have no experience with more modern synthetic materials. But a cotton undershirt, thick, thin, sleeveless, long sleeved or short, will become very uncomfortable if you break a sweat. If you're anything like me (you probably aren't), a two-mile hike on a windy 45-degree day with a pack will leave you with a damp undershirt. Of course, that only becomes a problem when you stop. The trick is to do everything to avoid perspiring and that's more important as the weather becomes colder. In theory, if one were on an all-day tramp with a stop to make camp in the evening, you could take off your damp undershirt and replace it with either a thin sweater or anything that's dry and be happy but I suspect most people wouldn't do that, including me. People seldom follow their own advice.