Even supermarkets are starting to keep more than just Red and Gold Delicious, which, although they keep well, are rather bland-tasting. Buy more apples in the fall, when they are harvested. Go to a local farmer's market. Local apples will always be tastier than apples stored for months and brought in from far away, and you might find some interesting new types. Store apples in a cool place.
Green apples are usually tart.
Granny Smiths and Pippins are two common green apples. Tart apples are often used for pies. Good, sweet eating apples include Fuji, Gala and Jonagold. Good eaters with a tart edge include Winesap, Northern Spy, Jonathan and Russet. Inc. How things get done.