I reenact the 13th century pretty well and have pics of my kit all throughout this whole site. However the guy to ask for that would be Joe Metz who has his Flickr album. He's the one who basically inspired how I wanted to do my kit, as theres many similarities between his kit and mine though I would say his is probably better than mine we're pretty close and similar with what we used.
Heres a pic of him and I with me in a nearly complete kit, only thing missing was a sword and thats only cause I didnt have the belt, so I used a mace instead, at the moment I do have a sword belt of the 13th century with an older 12th century sword being used in the late 13th.
http://www.flickr.com/photos/8765199@N07/10596356694/#in/set-72157637221932746/lightbox/As what Ian posted with the knee cops and shynbalds being used in the mid 13th I went that route because I couldnt get my chausses on myself as they were tie in the back and they were too big. I am currently working on trying to tailor the feet, I sealed the backs up with riveted links to convert them to full leg ones as they were a bit oversized on my legs. Thats what Joe did with his too which him and I being nearly the same size and build worked for both of us, not sure if it would work if you're anybit bigger so I'd suggest full leg ones anyway if thats what you want. Tie in the back are simply less convenient.
Helmets wise I would suggest a great helm similar to ours though I own 2 rather fine ones I didnt want a cheap heavy GDFB one as I don't plan to do any fighting in my kit apart from cutting demos. Royal Oak armory's great helms are probably the best you can get on this side of the pond their dargen is the best replica I have seen, I also own the Madeln Great Helm as well.
Maille wise I would suggest round riveted round ring with alternating flat punched rings, as thats what most of Europe used, if you're doing Germany like I am then you can get away with Wedge riveted which first appeared there in either the 1220s or 1230s, it did NOT spread outwards till about 1300. Avoid flat ring round riveted as that stuff is rather inferior in quality and looks nothing like the real stuff. Wedge however I have seen examples similar, round ring round riveted I also have.
Shields wise you can get away with a kite early on or a "converted kite" similar to my teutonic shield. Later in the century they got smaller due to plate becoming a bit more dominant, you wont see it in many art examples but in effigies there are examples of early coat of plates as early as 1250, I wouldnt recommend it if you're not used to tons of weight, I can wear my maille just fine but coat of plates over maille is rather heavy honestly. Most of the visby armor dates to about 1290 and was long outdated in that era as Sweden was quite poor.
Swords wise you can get away with anything between a type X and a type XIV for the 13th though germany tended to hold onto older designs more along with crescent pommels which are hard to find in modern repros.
Hands armor wise both mittens and gloves made of maille existed. I use gloves but plan to eventually make integrated mittens for my hauberk.
Coifs were mostly integrated until the later half when separate ones started making a comeback. I use a separate one that dates to the early 14th century. Joe Metz uses a separate one too but tucks it in to give the illusion of an integrated one, I'd suggest doing that and you HAVE to tailor them to make them "look right".
Hope this info helps, this is most of what I know about the 13th century it being my period of interest the most.
