When you go food shopping (my local ones are; Lotté Marte or Home Plus: aka Tesco), the Koreans seem to be very conscious of the environment, as they hardly ever use plastic bags (they sometimes charge you per bag). I recommend taking backpacks or bags for life when shopping. 
Although, when you go shopping you take all your stuff out of your trolley, just to put it back in and then pack it into cardboard boxes, provided from the supermarket. They also provide tape (as boxes are flat packed), scissors (to cut the tape) and even plastic ribbon to help close up the box if you pack too much in it... Which most weeks happens to Paul and I. However now we have a good stock of food that will last a very long time. If you go to home plus, they also sell Tesco own brand food, which when on offer I would suggest bulk buying as it doesn’t stay on offer for very long. 
I would suggest going to a market for fruit and vegetables, as the supermarkets can be overpriced. However sometimes they will have special offers and it’s your choice where you buy them from. Both fruit and vegetables are expensive, but buying from the markets will make a difference in your purse. Also if you can, buy bread from a bakery. The bread in Korea is pretty sweet as it is made from milk and sugar. Granary bread is hard to come by, but the bakery should have some and this doesn’t taste as sweet as the white bread. Some do come with currents in, so be careful when buying! From going to the same bakery most weeks, Paul and I were given a free tasty treat (which was amazingly good!). Sometimes at the market they will have homemade tofu, which tastes a lot better than that bought at the supermarket. 

From what you cannot find in the supermarket, or whether it is ridiculously overpriced I would suggest importing it. I use a website called iherb.com which is exported from the US. Sometimes buying food this way is cheaper than buying it in the supermarkets (and that even includes the delivery fee). Orders do not take long to get Korea, so this is worth looking into.