Another vote for Keepers, fantastic nursery, I've used them for fruit trees for 9 years.
If you want to maximise your growing season, it depends where you are. Here in Kent our season is very long, I don't have to worry too much about frost getting the blossom. This adds more flexibility, without knowing where the OP is, it's very hard to explicitly recommend varieties.
I've found both Discovery and Reverend Wilks tend to work very well for early season. Have had Discovery store till Christmas, wrapped individually with news paper, in a cardboard box in the porch.
You can store apples by canning/bottling (either as apple sauce, or larger chunkier bits), freezing, drying, or just as above, wrapped in paper in a cardboard box in a dark well ventilated place.
Good luck and happy growing.
Julia