As far as breeches go, I feel your pain. All of mine are cotton except for the pair of FITS and the pair of Struck breeches I bought on ebay. Both the FITS and the Struck feel amazing on and let in plenty of air when I stood outside in the wind. However, I am saving them for shows, so I won’t be able to tell you anything about them for awhile - plus new, neither pair falls in your stated price point. All of the cotton ones I have are gross when they get sweaty, but the ovation pull ons are the grossest. The Devon Aire Versailles are the least gross, but are so thin that I have to wear Spanx underneath them in public, which defeats the purpose entirely (they get worn at home). The best compromise between comfort and coverage that I have is the Ovation Celebrity Slim Secret. They have some kind of finish or thread in the fabric that makes them stay dryer than the Ovation pull ons. Also they hit my waist in a good place (I can’t wear low-rise anything).
From feeling of them in the store, I think the Kerrits tights are probably pretty comfortable. I am too lumpy to feel comfortable wearing in them in any color other than black so I haven’t bought a pair.
Show shirts - I saw the a shirt at a tack shop that had old-school cloth neck, front, and cuffs, but mesh fabric on arms and on side panels. I am pretty sure it was the Ariat Triumph http://www.sstack.com/apparelboots_english-clothing_ratcatchers/ariat-ladies-triumph-show-shirt/
This appears to be a pretty good compromise between coverage and cling. My issue with them is where they are mesh, there is nothing soaking up the sweat, and if I was to get one, I will probably ruin the inside of my show jacket (I don’t have the figure for stretch/washable jackets).
I have an Essex CoolMax old-school cloth show shirt that I wear when I’m riding outside, to keep my forearms covered, and I love it. It was really expensive new; my sister gave it to me after she spilled coffee on it. There is something in the fabric that keeps if from getting / staying wet. I bought another one, new, for $25 on ebay and am saving to show in. I think there will be more to come on ebay since so many people want nothing but the stretch shirts.
The thing I don’t like about the Essex shirt is I think it’s too fitted in the waist for my figure. I prefer a straighter cut. The upside to the Essex is it actually has room for my chest and buttons in a good place across the chest, which is rare for me to find in a show shirt. I think Tailored Sportsman also made a coolmax shirt, and it was straighter cut. If I’m wrong about that, somebody correct me, because I have an ebay search set for the TS shirt (no hits yet though, so I may be wrong about that).