The closest supermarket to the university is a NETTO in the pedestrian precinct, called “Milchstraße” near the Malteserstraße. Often crowded with students – includes bakery and lunch snacks. NETTO calls itself a “brand-discount”. This means, that unlike many other discounters they also offer brand products like for example beer from Warsteiner, Bitburger, Früh, Becks …
Only a hundred meters further and very close to the Bus Station “Drischer Gässchen” is REWE. Most of the products are more expensive than in NETTO or Lidl, but you might need to come here if you are searching for a special spice or other weird ingredients.
From my experience the cheapest discount supermarkets are Lidl or Aldi, but those tend to be further outside the city and they do not offer many brand products. Nowadays those supermarkets also offer daily-freshly baked bread much cheaper than in a usual bakery.
Other widely spread companies are Kaisers or Edeka. You can decide for yourself whether you think that the additional quality is worth the additional price. Kaufland is the biggest shop I know in the region.