Welder Dan makes great points. Knowledge is key. I've done lots of reading on wild edibles but don't think I will be getting into mushroom hunting anytime soon. Too risky unless you have an expert teaching you.
Wild game is a great resource but there's something called "rabbit starvation" or "protein poisoning". It's basically a form of malnutrition caused from lack or fat. Wild game is extremely lean. You'd be best to supplement it with wild fish if you can. Anyone know of any wild animals with high fat content? Duck and geese maybe?
You are 100% correct regarding eating rabbit exclusively. Your body needs fat. Squirrel is fattier than rabbit. Duck would be ideal with it's high fat content, and it's yummy. Fish is a good source of good fat. Possum is extremely fatty, and they are stupid and easy to catch. Beaver is also fatty. Nuts are probably the easiest to get and they keep well. Walnuts, pecans, hazelnuts and chestnuts are widespread. Hell, pot seeds have fat! Avocado is a also a good fat source.
Then there is wild hog. They are literally everywhere, but they can be extremely dangerous. Best to have a rifle. And in drier colder climates, you can air cure the meat with salt and it keeps for months.
Which leads me to another good subject. Curing and smoking to preserve larger game. Those are very old methods of preservation and well worth learning.
This kind of knowledge is slowly being lost. Humans did this as a way of life for thousands of years. Now most people would starve.