When I was young the everyday meats were beef, lamb and pork. Chicken was a rare treat for a Sunday lunch.
You're showing your youth. Mutton was a common meat back until the 70s. Lamb was a seasonal thing then. I was glad that mutton disappeared. The taste wasn't great and the grease stuck to the roof of your mouth. Prince Charles tried to revive it a few years back. Veal was popular at Whitsun and was excellent, but people were put off by the methods of husbandry.
I could never see why horse meat was so disparaged in the UK. I've had it in France and it was excellent and very tender. Here's an expression to keep things on topic, "This steak is like a piece of horse meat", meaning it was tough.
For pheasant, there's too little fat in the meat to roast it successfully. It turns out dry. You can drape it with bacon and put an onion inside it, and it's OKish. Casseroling it is the best, and in that case, you may as well skin it and cut off the wings and legs with secateurs. Casseroled skin isn't up to much and it avoids the work and mess of plucking it.
Duck's a different thing, not that much meat but the skin, properly done, is the best part.
When I was a kid I knew someone with a game cupboard - perforated zinc sides and the birds hung on cup hooks. They liked them properly gamey (rotten) but I don't believe they ever had them dropping off the necks.