I used to like Granny Smith they are a pretty good apple in a pinch for me these days but my favorite these days is Cortland, macoun then McIntosh. Those are some delicious ones! They aren't as tart as granny is but they have a better flavor that's hard to describe.
We eat them raw mostly. I do cook some here and there but we cherish them for the wonderful fiber and different stuff that's best consumed raw. When my son gets older we will likely do some baking of them but he’s not quite interested in the cooking aspect at the moment, he just loves them sliced up lol. I try to reinforce his indulgences like this as often as I can!
My favorite for apple baking is to make a crisp. Brown sugar, oats, a little flour and butter. Mix it up and put the apples in a glass 4x8 pan and sprinkle it over top - wonderful stuff!