Potatoes -- good, but they work well for me one year and were awful in subsequent years. Probably the wet/cool weather we had a couple years ago. They took up too much space for me for such a small return, but I'll try them again sometime.
Tomatoes -- try a variety like Big Beef, or most any variety with "Mountain" in it's name. You'll want to look for the disease resistant varieties if disease takes over your plants each year. Nobody I know has had consistent results with Better Boy or many of the main kinds they sell as plants at stores. If you want to go heirloom, try Black Krim -- usually the first in my garden to produce, and produces a lot!
Beans (snap beans) -- try a bush bean like Contender or Provider, or to save space try a pole bean like Rattlesnake. Rattlesnake beans do awesome, and I usually have to pick the beans every single day to keep up with them. The vines for me usually climb up a 7ft fence, and all the way back down again.
Squash -- I prefer the flavor of yellow crookneck squash. But whatever you do, plant squash/cucumbers/melons/pumpkins from SEED -- do not buy plants for them at stores. Melon seed, for me at least, always do 200% better than bought plants. It's amazing how much difference it makes.
Pumpkins -- To save space, try a semi-bush variety like Gladiator, which is also somewhat resistant to powdery mildew (they still get mildew in my garden in the humid summer with afternoon thunderstorms, but by the time it hits, the pumpkins are almost ready to harvest). I plant my pumpkin seeds around the end of April for the Raleigh area, and I usually pick my pumpkins around the 2nd week of July, wash them off with a bleach water mix, and store them in a dark closet indoors. They will still keep through January. Planting early also helps the plants get a jumpstart on the squash bugs, which show up for me around the end of May or early June. By then, pumpkins have already set and are steadily growing before the insects hit hard. I also tend to plant a trap crop of yellow squash -- the bugs in my garden always go for the squash plants before hitting my pumpkins. I also plant marigolds throughout my melon plants. Whether it helps or not, who knows.
Cucumbers -- Arkansas Little Leaf has very small leaves, compact vine, and doesn't need good pollination to set fruit. Try a variety that is compact/bush or intended for containers
Okra -- try a cowhorn variety, and you will have okra stalks about 7-8ft tall that grow all summer. I've also noticed that with the cowhorn varieties, you can let the okra pods get larger than with the common clemson spineless, and they wont get woody as fast.
Peppers -- bell peppers are hit or miss for me. Some season they do well, some seasons I only get 2-3 from each plant.
Purple Hull Peas -- always do well for me, are very forgiving of growing conditions
Watermelons? Look for a compact or semi-vine or bush variety to save space
Cantaloupe? Same, look for compact/semi-vine/bush
Sweet Potatoes? Long vines, morning-glory-like flowers
Corn? I never have luck with corn because it requires a LOT of nitrogen and water. My neighbors, however, always have corn plants that are seriously 10 foot tall with ears of corn almost the size of footballs...
Plant some marigolds and zinnias or other annual flowers in and around your garden to attract the butterflies and bees and other pollinators. Keep-up with fertilizing and providing enough water. And if you want to bump-it-up a notch, look into a fungicide routine if your garden usually gets hit with disease early in the season. But most fungicides only work as a preventative... if you wait until disease already starts, it's typically too late!
Spring and Fall stuff (I plant most of these in August/September for the Raleigh area, which allows them to mature in cooler weather):