All the things you mention can be started in may or june. Maybe throw in some tomatoes. The peas can be started early (late april) as they are frost tollerant and enjoy cooler weather. Carrots, radishes, and cucumbers are easy too. I grow in a little different climate than you wet siders so I would take the local advice.

Make sure you have a plan for pests. Deer, birds, rabbitts, bugs, bugs, bugs. The best thing I done for bugs is to have boundaries of where they can be helpfull and where they are not allowed. I allow them to thrive in my compost but poison the flippers arround the plants. Talk to the people at the local garden center and they will tell you what kind of bugs to look out for in your area. Starlings will eat your corn when the ears get just right. Those suns a bitches got me last year real bad. I had never had a bird problem in 7 years and thought the fricks were eatin the ear wigs. Nope they ate the tips off every ear.