What are budget groceries you buy in America?

Dried beans. Rice. Chicken thighs. Frozen or fresh vegetables. Make soup for a week. You'll be sick of it by Friday, but you won't starve. Currently working through a pot of beef, cabbage, and potato soup.
- Cabbage is so great!

Often it is not just about types of food but where you can go to buy it.
Which depends heavily on region (the USA is ENORMOUS, literally thousands of miles separates e.g. Texas from New York City), but Trader Joe's often has high quality foods for lower prices (and such variety too! Not so much week to week but different than regular stores, like international foods, and more optimal for a single person portions, but still has things like packs of frozen chicken great for families). But "very little money" might exclude that, for a family and especially one that still needs to visit another store bc TJ's does not have everything (I wouldn't purchase toilet paper there, as it would be more expensive than regular grocery stores iirc), so the time and travel burden of visiting multiple stores can be prohibitive.
At which point I think of Aldi's (owned by same parent company, in Germany iirc) - if you happen to live near one, then regardless of how much money you have available it is always highly recommended. Somewhat similar concerns about multiple stores though.
As for types, others have said already - beans, chicken, rice, etc. Much of that could change in the future as a result of tariffs.
- Aldi and Trader Joes are separate companies owned by brothers in Germany. They are both very low prices, but they are not the same parent company. Shop at whichever you have near you.
  
  If they're founded/owned by two brothers they just have a parent, not a parent company
  
  To be specific Aldi in the US is Aldi Sud while Trader Joe's is owned by Aldi Nord but operates separately.
- Ethnic grocery stores almost always have the best prices.

It's important to get stuff that lasts a long time. Make sure all your dried foodstuffs are stored in airtight containers. If it's spoiling or getting infested that's wasted money.
Stuff I bought while in college: dried soup (the cheap Mrs Grass crap) or Rice-a-Roni can be stretched by adding extra egg noodles/rice. And enhanced with meat/frozen veggies. Hamburger Helper, but only when on sale.
Buy meat in family packs, freeze it for use later.
Those little refrigerated tubes of dinner rolls are so versatile. Butter them and sprinkle with garlic salt before baking for garlic bread. Butter and cinnamon sugar for dessert. Marinara sauce/cheese for tiny pizzas.
Kool-aid instead of soda.
Pasta dishes. Spaghetti, macaroni, noodles. A pot of macaroni with just a can of diced tomatoes can be really satisfying. A pot of rice with just tomato sauce.
- Kool-aid instead of soda.
  I bought a tub of electrolyte powder for $15 when I was sick and drink it often now. Tasted really good and doesn't need 2 cups of sugar added so I'd recommend it over Kool aid for both health and cost reasons
  
  I can bulk buy stuff at my local co-op, I'm lucky to have one, and they have dried hibiscus flower fairly cheap. I boil about a half a cup of the dried flour with a gallon and a half of water, with about 3/4 cup of sugar, adding lime juice at the end. It's like adult Kool-Aid. I love it.
  
  Could you be more specific?
- Don’t forget beans, really cheap protein

dry popcorn, potatoes, bulk rice, dried beans, onions, garlic, vegetable oil, salt, black pepper, chili powder
rice and beans will get you the full range of necessary proteins and the rest will fill you up
I was surviving like this on 50¢ a day back in 2009. Lunch was always popcorn.
Of course, now I know how to use food banks, and with food banks you can get greater variety (and some fruit for vitamin C) for even cheaper.

Rotisserie chicken. $5 for an entire cooked chicken with the skin and bones. Enough meat for four meals plus it can make a decent amount of chicken stock.

I eat a lot of Mexican cuisine because the ingredients are cheap, easy to keep, simple to cook, and taste awesome. And being in California, there's plenty of local Mexican grocers to get stuff cheaper than big box stores.

Mashed potatoes is my thickener of choice. Add it to any soup/chili recipe to make you feel full without spending a lot.
- Are you referring to the boxed mashed potato mix or real mashed potatoes? I could see either working so I wanted to double check
  
  Either one. Boxed is faster but real tastes better

Make sure you know how to cook. Even a simple pan over a campstove (outside!) will make your meals much better. The basic ingredients are always much cheaper than the per-prepared stuff, and generally healthier. It is more work, but often not as much as people think to make from scratch. Go your local library and find a cookbook and make something from it. Then next week get a different cookbook...
- This is something I am eternally grateful to my mother for teaching us. I am no Michelin chef, but I have managed to develop a few "signature" dishes that friends and family rave about. It's pretty easy too; it's actually pretty hard to fuck up a dish in such a way that it's inedible.
  There's something really relaxing about cooking -- the ingredients changing the overall look and texture as they cook, how you can alter the flavour entirely with just a tweak of the spices... and the best part is that you (almost always) get to eat it. And there is something very calming in the knowledge that you can make something edible if not delicious with just a few inexpensive ingredients.
- Knowing how to cook is really the first step of saving money with groceries. This advice can't be understated

grocery outlet, despite most of his inventory is constantly shifting, near expiration, it can be cheap depending on what you buy. walmart is just too far away. and tar'ge is not exactly cheap.

I can get a loaf of bread, or donuts, or bagels for 1.25, but i live near a bread outlet

There too many different variables. There’s people who buy their coke, Doritos and Oreos and there’s people on the latest trend of diet and then those who are veggie/vegan and those whole eat healthy and then those shopping what’s are dollar tree. You should be getting many different answers.