Oh wow. I love Connor's design, and while I don't have any intentions of making this costume yet (though, I feel like a friend of mine may want my sewing help..he loves Connor and the concept as AC3 even more than me), I love this thread, and I love, love how the OP is keeping historical accuracy in mine (well, as much as one can). Haven't read through all these posts, so forgive me if I'm repeating any info!
1. Do absolutely make a shirt to wear underneath. Yes, a white tee is better than nothing, but most knits can't wick away sweat and heat like a good woven fabric. They wore many layers and lots of wool, back in the day, even in the summer, and they had no AC. Yet, they did not piss and moan, at least not more than we do! Basically, a plant fiber layer close to your skin pulls the moisture away from you--plant cells have evolved to do this. Linen is best, bust cheap ass muslin in fine if you're on a tight budget. The idea is something made with natural fibers that you can throw in the washing machine--it'll protect your outer layers from your BO so care will be easier. here's
instructions for an easy to sew (though the math is tricky) and very period correct 18th c men's shirt
2. fabrics-store.com is probably the best place to go for linen. I've bought a lot of linen from a lot of places, and this is the best bang for your buck. Keep an eye on the sales, and, sometimes you might be luck enough to get a card with a coupon code tucked in with your order invoice...Nice!
3. Wool will always be cooler than synthetics. If you can't afford wool, try to make a cotton or linen work. A costume like this requires layers, You will MELT if any of these layers are polyester!
4. Still think wool's out of your budget? Don't give up yet! If ordering online is your only economical option, get the minimum order first. Admittedly yes, 20$/yd is a decent price for wool, and the absolute best you can hope for is usually 10$/yd, but personally, I feel the cost is worth it. Wool does things other fibers cannot, and I firmly believe there is no substitute. Of course, it's your call. Before giving up on wool, I recommend getting in touch with your local International Costuming Guild branch and asking if anyone has any leftover wool in their stash (at least at NoEL we had lots of people wanted to get rid of stash!), in which case they'll probably sell for cheap, or ask if there's a mill nearby where you can get "mill ends" for stupidly cheap.