I think a mile is far enough away. I've never personally gardened near the ocean, but unless the soil is heavy with salts, or the spray actually permeates the air around the plants, I think everything should be okay.
I think your best source of specific information would be the nearest Extension Service office. They will be knowledgeable about plant varieties that do well in your area. If there is no Extension Service office nearby, you could talk to the staff at some local nurseries or independent garden supply stores. Local nurseries and independent garden stores usually carry varieties that will succeed for their customers.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams