One of the biggest shockers for me was how much I spent the first month on just basic life things like shampoo and school supplies because I did not bring those to Europe as it would have made my bags weigh more.
In Salzburg especially some college student budget stores are EuroSpar, Billa (for beauty supplies), Lidl, and InterSpar. Try to stay away from the touristy street, Getreidegasse where things are crazy overpriced. Definitely head over to EuroPark the mall where all of the Austrians shop, prices will be cheapest, but most of the time it takes a bus to get there so be ready to pay.
Something to note is that you will not be able to buy anything in Austria on a Sunday. Nothing is open. Literally nothing is open. Most stores close by 7pm so make sure you get your groceries in the morning or during the day! Also, you have to pay for a grocery bag in most of Europe and especially in Austria. So unless you want to pay, you need to bring your own bags. Be sure to be speedy in putting your items in your bag even if you have someone check you out because it is unacceptable to be holding up the line. (This is very Austrian!) Nobody will bag anything for you.
You will have to "rent" a grocery cart also, usually costing a 50 cent Euro coin to get the cart out and then when you return it you get it back. Also you will learn that very few places take our American plastic whether it is credit or debit, they want cash.