I know if I were doing that I would be taking a lot of the kinds of stuff I take backpacking, and some of the bulk foods I make at home that are cheap

spices and stuff (chili, salt, pepper,curry, garlic, etc)
potato flakes
onion flakes
pasta
couscous
ramen
mac n cheese
rolled oats
peanut butter
lentils (they cook fast!)
chicken soup/stock mix (for soup or cooking)
coffee/tea (I'm addicted)
olive oil
garlic
beans


I'd probably take a bunch of canned stuff,for easy meals and variety. a few dozen cans of stew, chili, tuna, corned beef, and canned fruit (pineapple, peaches, etc.) and some pasta sauce.

I'd pick up the odd loaf of bread as I went along at a convenience store. still cheap.

I'd then chuck in a pot to cook in, and something cheap to cook on. I would probably take a white gas stove, because enough fuel for a month is not very expensive, and I wouldn't have to fiddle with finding wood or whatever where there wasn't any to
be had.

I'd also take a bunch of 2l pop bottles to have for water stowage, so I could tank up at rest stops that had potable water for drinking/cooking.

But a lot of it will depend on your ability to make stuff you like out of simple basic ingredients.

but have fun. sounds like you've been thinking about it and you will.