Welcome to the forum Weefey
If conditions are warm enough the snap beans (aka green beans) will do well. I grow the bush variety because of the low ceiling height in my greenhouse. Blue Lake bush beans, and Royal Burgundy, I also grew Calypso beans (aka Orca beans).
Although I don't grow many peas, pretty much anything you grow in soil you can get to grow in AP. If you have troubles you can always setup a wicking bed. I find grow beds and wicking beds complement each other because the wicking beds warm a bit sooner but it may not matter in your area as much.
edit: Forgot to mention. I usually do two crops, an early and a late one, both in the greenhouse. The reason I do it this way is spider mites get really bad and start to wipe out the bean crop when the weather gets warm. Rather than spray I just rip the beans out and leave the space empty for awhile before starting a new batch. Seems to work pretty well and I get quite a few beans without much effort.