You should wear whatever clothing you are comfortable in and allows you to work hard without overheating. Overheating is bad.
I'd suggest clothes made out of lightweight 'tech' fabrics such as Nike Dri-FIT, Adidas ClimaLite, Brooks Equilibrium, Asics Hydrology etc... I'd avoid anything made of cotton because cotton gets really heavy and clingy when you sweat.
For indoor cardio, I wear a pair of briefs, a pair of lightweight loose exercise shorts or running pants, a short sleeve t-shirt and a hat (lots of hair to control!).