The upper undergarment for Medieval people is a linen shirt. 
No doubt details changed through our period, but there is evidence for short slits in the sleeves, and arms that end midway down the forearm - this is possibly a reflection of some of the styles and techniques used on the braies. Clothing in general was not cut very flatteringly throughout the 13th Century: for example advanced darts and gores seem to be little used, and it would appear that seams at arm/body joins were straight and not curved. (Simple gores - large triangular inserts of cloth - were, however, common ways to expand the hems of cottes and dresses from handwoven fabrics that would rarely have exceeded 1m or so in width).
For everyday wear, a cotte or tunic would be worn over the undershirt. This knee-length woolen garment was the standard clothing for all levels of society although, of course the quality of cloth, the colour and the standard of decoration applied to hems and the like would vary. The cotte had long sleeves that ran fairly tightly down the arms, and often ended with a slit at the wrist. The neck opening was often like that of the undershirt. Our knight would get too hot fighting with this extra layer on, so it isn't shown here.
On this knight's head is the first layer of head protection. This coif is padded like the cuisses, and in style it is just like the normal white linen coif worn by all men during this period. In poor weather, a woolen hood (with a relatively short liripipe) would be worn over the top.
The padded coif that I have made is comfortable and effective, but remarkably good at absorbing sound when worn on its own.