My parents always kept a bottle of lye water in the cupboard for Zongzi, to soak the palm leaves in for a traditional Chinese glutinous rice "tamale" (I miss eating these very much). My father was fond of Thousand Island Russian dressing that went on iceberg lettuce when it was steak night (followed with fruit cocktail in a can for dessert!) I've never attempted Zongzi, and I don't like Russian dressing!
I've kept a container of my MIL's oregano from well before the 1990s, it seems like it never runs out but it's at the point where I could transfer it to a shaker.
If you are going to do any cooking as a student, then things like pasta, onions, potatoes (tubers) and a fridge are going to be your best friends. You can buy bulk meats, divide them up and freeze them for individual servings. Buy bulk toilet paper, etc and save on those, especially if you have a warehouse store in the area.
One package of pasta at $1, a can of tomato sauce simmered with onions and other fresh veggies ($1-$4) will give you 8 meals (or roughly 62cents per serving); so cooking half a package or even a 1/4 package of pasta can be scaled, with the rest of the sauce stored in freezer. If you go to a restaurant for one serving of pasta, that easily costs $8 or more. One frozen pasta serving will be $5-6.
I've been feeding a family of 4 for the last 10 years frugally this way and we do takeout on Fridays. The idea is that you are prepared to have the same meal possibly twice, or 3 times a week.
Once you figure which produce you enjoy the most, and fresh produce can be had cheaply even if you shop every week.