Jerod, I don't have an answer to your corn question, but likely fellow vegetable farmers will chime in.
Your proposed garden sounds like fun with a high success rate - all are summer crops so wait until your soil and temps are warm enough. Maybe toss in some sunflowers for a bit of pop. Pumpkin, corn, and green beans are often grown together - pumpkins at the foot of corn, beans using the corn to climb.
