None of this is in any way official. People should edit and revise it based on the collective consciousness of the society.
TT Runs on Tropes: In almost all cases, the trope should overpower any specific details. If you are playing a Norscan berserker, the trope says hulking, furs, possibly no shirt. That isn't really 'historically accurate', but the trope is key here. The flipside of this is that trope itself needs to be appropriate. A victorian mad doctor is a cool trope, but not really a good one to play in a medieval game without serious adaptation.
Natural materials: One of the nicest ways to make your kit more pleasant to wear and also more 'IC' is to try and get stuff made out of natural materials. Linen shirts are amazing at wicking sweat and generally staying comfortable while active and fighting, wool outer layers are a great balance of warm and relatively wind/waterproof and also reasonably breathable in hot weather (which does happen - while we spend most of our time playing in the winter, it's useful to consider the summer term before you make a fur-lined jerkin for your new scout to wear under her heavy cloak).
Safety and comfort first: This is an outdoor, active contact sport. Nice authentic kit is cool and fun. Shoes you can run in and clothes that protect you from things like nettles and barbed wire, however, are generally a higher priority.
TT is nominally set in 1296 (as of this writing) in a magical medieval fantasy Wessex. So there's not really a distinct historical period, more a huge pile of medieval fantasy tropes all crammed together into one game, with all of the costume they imply. The best rule of thumb for kit is therefore basically "would this fit well into Lord of the Rings, Warhammer, Game of Thrones, or the like?" Tropes are cool, but some tropes aren't really medieval fantasy.
On the late end of the period, we've had swashbuckling musketeers and the like, which just about fits in. The 'line' is roughly around the frockcoats and tricorns sort of point. Frilly shirts and bucket top boots can be in, but are a bit on the edge, while going beyond that, into frockcoats, is getting decidedly past renaissance. Obviously, going further into steampunky or victorian styles is also not really optimal.
On the other end, it's really quite hard to wear kit that's too early for TT. The early medieval look that's perfect for slightly lower-status characters is one that's very generally applicable pretty much all the way through the dark ages. As long as you stay out of roman kit, you're pretty much okay.
So, what to draw inspiration from, now that we've got some rough boundaries? A very loose set of times to go for would be pretty much anything that's dark ages, early medieval, or high medieval. Say roughly 500 to 1500 or so. This is an extremely wide range of things, but some specific stuff which makes good kit from these times includes:
Tunics: Tunics are great. They're easy to make, comfortable, can be warm (if wool) or nice and breathable (if linen). Tunics are relatively speaking quite an early garment, but they're great for commoners of various types all the time. One thing which looks really cool and is quite easy is to pair a long-sleeved undertunic (perhaps in linen or cotton) with a short-sleeved overtunic in wool. It's also great warm kit for linears.
Doublets: The other classic medieval garment is the doublet. These are a bit more complicated to make yourself, as they tend to be closely fitted. Doublets are often fastened either with lacing or points, or with lots of closely spaced buttons.
Surcotes: A big thing in medieval clothing is layering. The idea of hanging around in the pub in just your shirtsleeves was really not on - its about as indecent as wearing just a bra is nowadays. A slightly fitted, sleeved surcote is a quite easy thing to design, and will give you that layering thing very quickly.
Trousers/hose: Pretty much the best thing to go for here is plain linen trousers. I got mine from M&S, but most shops (Primark, Matalan, etc) will start stocking them shortly. They're not ideal for everyone for larp, but they're a pretty good generic looking baselayer. Making some form of leg-wraps is a great way to disguise nearly any trousers, especially if you're aiming for an early peasant type of outfit. Hose are quite an involved thing to make a nice pair of, but patterns can be found if you fancy trying it. Otherwise, especially if you're wearing several layers, plain thermal trousers work well as hose, especially for interactives.
Hoods are really cool. Head covering is a very common thing in the medieval period, and a nice hood makes even fairly basic kit look very IC very fast. They're also quite cheap and easy to make, so an excellent learning project. Medieval hoods tend to be separate garments more than they're integrated. One awesome way to make a hood look medieval is to make it with a long liripipe, where the fabric of the hood extends into a long tail that can be up to five feet or so in length.
Narrow but long belts. Leather isn't exactly cheap now, but it's a lot cheaper than it used to be, so medieval belts tend to be quite narrow. On the other hand, they also tended to be quite long, and the custom was to tie the belt back through the buckle and let the rest hang downwards, instead of tucking it away through belt loops.
For fastening, buttons were generally uncommon. What was a lot more common was lacing of various types. One way of lacing things which is quite easy to retrofit onto an existing garment is to use 'points'. Fit pairs of eyelets into both sides, and use short sections of leather thonging tied through them to fasten the pieces together. This ends up working much like buttons, but looks very iconically medieval for not too much work (fitting eyelets into say the front of a waistcoat is doable at an interactive).
http://www.profounddecisions.co.uk/empire-wiki/The_Marches_costumes
http://www.profounddecisions.co.uk/empire-wiki/Dawn_costumes
http://www.profounddecisions.co.uk/empire-wiki/Wintermark_costumes
http://www.profounddecisions.co.uk/empire-wiki/The_League_costumes
Medieval Tailor's Assistant
Re-enactment group websites for middle ages (pre ECW)