Sunforger treated canvas would be best. Panther Primitives are great folks to work with, and they do additional business selling trade-ins., so maybe you can find a good deal by asking.
If you can afford it, I'd pay a bit extra and go with the small Sergeants tent with short walls. That's just about the same floor area as a wedge, but a bit more usable space and HEAD ROOM. After several years of using my wedge, that is what I missed most, the lack of head room except down the middle.
Also, if getting a wedge, get one with tent flaps on both ends so you can get some cross breeze. Mine has only the one end open so can get a bit close. Do get sod cloth flaps sewn around the bottom edge, and a treated ground cloth (and a plastic drop cloth to put under your floor to minimize dampness). My wedge is very easy to set up by myself, but truthfully, I've seen just about every combination and size of tent put up single-handed. For that matter, a pyramid is a very good choice, too, and only one pole to fool with.
As far as winter season camping, adjust your camp bed for warmth. Add blankets, quilts, a buffalo robe, etc. Not much to do to make the tent more winterized, unless you add a stove. And while some swear by them, most stove and stovepipe arrangements left much to be desired. Besides, events are not planned in the Winter, usually.
Stay away from fantasy tents like that so-called Sutler's tent, especially for NCOWS. There is still controversy over such tents, sometimes called a Baker Tent, as to finding actual documentation of their existence in the 19th century. Besides, an open porch is an open invitation to 'skeeters. You can always add a fly to any tent for a shaded porch.
Also a tip: take a wax candle and rub along all sewn seams on the inside of the tent. It helps to seal the needle holes against rain drips.
I own a KIA Sportage and can transport my whole camp and gear. My wedge poles were made by me so I could hand pick the lumber at the lumberyard, and are two 2X2 uprights and a ridge pole made by glueing and screw two 1X2 to form an inverted "T" of one piece length.
RCJ