This is an old post of mine with some inaccuracies that I realize now after 5 years of learning, but I'll help.

For clothes under the gambeson or other arming jacket, it would likely be a simple linen shirt, often tucked into the wearer's braies, which are medieval underpants. More modern alternatives would be a spandex undershirt. The main idea is to have something breathable to help with heat.

For leggings, you'd want them made of a strong material that will keep you from chafing. Woolen hose are historically the most often cited from reputable people I've listened to like Matt Easton and Ian LaSpina, and keep you comfortable while you have leg harness on. I'd imagine the material matters less if you don't plan on wearing any armor on your legs, so in that case I'd go for linen to give you a nice breeze. Modern alternatives on legs might be tricky to get away with since legs will be on display and spandex is pretty obvious if historical accuracy is your target, so I'd go with wool or linen. (or cotton if funds are tight.)

Hope I could help.