Tight fitting, machine knit cotton undershirts had become common by the start of the Civil War.  You often see photos of soldiers in camp wearing this type of shirt as their only shirt.  This reproduction from South Union Mills is comfy, will keep you warm, and is useful for any impression.  And it is a much better option than a Walmart plaid "homespun" cotton shirt.
Available in size Regular (will fit up to a 42 chest) or Large (will fit up to a 48 chest).