When I buy apples I tend to buy the Granny Smith variety. I've heard that it's more of a baking variety than one for eating directly, but I like it better than others I've tried. The only two names I can recall are  Red Jacket and Red Delicious. I know there are tons of types of apple that I'll never eat unless I make an effort. Which types should I, as a Granny Smith fan, go out of my way to try? As far as I can tell I like both the acidity and the crispness of the Granny Smiths.  Wikipedia tells me that Granny Smiths "The tree is thought to be a hybrid of Malus sylvestris, the European Wild Apple, with the domestic apple M. domestica as the polleniser." I've been unable to find European Wild Apples nor any other varietals that are derived from them. 
Granny Smith apples are rather tangy. I would reccommend Pink Lady's or Braeburns.  Let me know if you have any questions 