I'm not sure I'm 100% qualified to answer this, as I'm still an undergraduate, but I'll give it a shot anyways. I'm also interested in the same time period and region and have done some independent studies on the subject for similar reasons.

The 1300s were the time of transitional armour in western Europe. From the mostly mail of the previous century, to the "knight in shining armour" plate of the 15th century. The change was gradual, and as they added more and more plate, weapons changed to deal with that, which just sped up the process.

The various body parts:

Limbs: Specifically in the Holy Roman Empire (HRE from now on) at this time, splint armour for the limbs was rather popular, despite full plate limbs being common in other areas of Europe.

Head: The great helm had gone out of style for field combat by this point (but was still used in tournaments) and was replaced by smaller helmets like the bascinet (visors were just becoming popular at this time and specifically the klappvisier in the HRE) and the kettle helmet.

Body: For torso protection, the coats of plates was very common for men at arms and the more wealthy would have full breastplates covered in cloth, both as decoration and as rust prevention (not to mention the fact that Europe was going through a 'mini ice age' at this time)over top of a mail shirt that went down to around the knees, or mail voiders (pieces of mail that attach to the arming garment to specifically cover places the plate did not).

All of this would have been worn over an arming garment such as a gambeson, aketon, doublet or many other names.

This is all specifically for men at arms and higher, the poorer might just wear a gambeson and helmet or even nothing at all (but most armies would reject those too poor to arm themselves).

References: http://talbotsfineaccessories.com/armour/effigy/German-Effigies.htm

http://effigiesandbrasses.com/

Sources: David Edge, Arms & Armour of the Medieval Knight

Claude Blair, European Armour