H Mart is my favorite Korean supermarket. It is big, bright and clean. The employees are friendly and they carry everything you'd need to cook Korean food.
Some of my staples are red chili pepper flakes, red chili paste, an assortment of mushrooms (king oyster, shitake etc), vegetarian dumplings, seaweed, bibimbap kits and exotic looking vegetables.
A lot of items don't have English labels but it hasn't been a problem for me even though I can't read a word of Korean.