To my understanding, the léine and the long shirt are one and the same.
I'd suggest that it might be up to your own personal interpretation as to when a long shirt becomes a tunic.
Museum specimens I have seen have always been linen, woven on a handloom, (obviously), and are the usual white/off white colour that you would expect from such a garment.



{EDIT} As far as I know, there is no evidence of tartan in the clothing found on the bodies.