I've always understood that beans and rice is the defacto struggle meal. It's hard to beat them for sheer dollars-to-calories ratio, and may even be less expensive than potatoes.
I'm sure you're aware - and I empathize with your situation - but eating a variety is best if you're able to manage it. Potatoes can go a long way to stretching a diet, but aren't very nutritionally diverse on their own.
A few less expensive supplements I've used in the past are peanut butter, and eggs. There's often a deal to be had by shopping seasonally - pumpkins are in right now and I get a surprising amount of mileage out of them.
Personally I love green onions with potatoes. They're not very nutritionally dense, but they're a pleasing aromatic and you can get a bundle for around a dollar. If you place your onions in an open jar of water on the counter, they'll continue to grow. I usually regrow my onions 4-5 times from a single bunch and plain water, a handy frugal tip
But assuming potatoes are the only or main item on the menu, there's an impressive degree of versatility in their preparation. Ultimately that usually adds up to mashed, baked, boiled, or fried.
Potatoes make an excellent soup. Even on their own - a local place here does a side dish which is just a quarter potato simmered in miso / vegetable stock. If you're doing other ingredients, the potato can be made into a thickener for soup - corn chowder is an inexpensive meal that I've leaned heavily on in the past.
If you make a large batch of mashed potatoes, you can repurpose the leftovers for other meals. Mix with flour and you've got croquettes or potato pancakes. You can pretty much just toss them in a pan and refry them. If fish is available to you, you can mince a can into a potato / flour mixture and then fry it to get a tasty fish cake.
You can jazz up a baked potato into what's known as a Hasselbeck potato if you want a fun presentation. Essentially you score the potato into several thin segments and drizzle it with oil while baking. It has a pretty unique look.
This last one is a bit off the deep end - but it's a local dish here and something that our family does for major gatherings. It's called Rappie Pie, or Pate a la Rapure, or sometimes Potats Rappe. It's a bit of a process, but the only essential ingredients are potatoes and soup stock. It can be a ton of work and not for the faint of heart, but it's a rather unique preparation and genuinely comfort food for me. We like ours fairly runny - we sometimes call it Potato Jello
This recipe appears fairly accurate, but I'll try to summarize.
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Grate potatoes into pulp then squeeze to remove the starch. This is the most laborious part of the process, so it's common for people to do this communally or to take a shortcut by buying a processed potato block.
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Gradually mix potato mixture into boiling broth. Whisk until smooth
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Pour into a greased pan, halfway through adding additional fillings if you have them. This is commonly served as a meaty dish with chicken, rabbit, or venison, but I've made it vegetarian or plain before too.
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Bake until a crispy skin forms. Serve while hot, leftovers can be frozen or refrigerated, then reheated in the oven or a skillet
Anyway, good luck to you. I hope food security is in your future, nobody should have to go hungry 😞