Any shirt longer than hip length becomes a nuisance under joined hose and leg armour; the few contemporary depictions of shirts bear this out. Old linens, btw, would be recycled as linen-rag paper.
A shirt with a belt over the top is fine if you want to play at being a pirate but nonsensical as period costume (what's holding your hose up? And if you're wearing split hose tied to the braies-girdle, why are you showing everyone your knickers?).