You don't have to wait until the last frost to plant spinach, lettuce, and onions for a nice salad. You can plant them 2-3 weeks before the last frost. Those are cool weather crops. You also plant a second fall harvest for those late in the summer. Those plants can stand a little shade, especially afternoon shade. With beans, tomatoes, and cucumbers, you have to wait until all danger of frost is past. They like full sun. You want to buy tomato seedlings at a store. With everything else, you can put seeds in the ground although they sell seedlings of all sorts of vegetables.
My mom lives on the Chesapeake in Mathews County up from Gloucester, and she has a garden.