With the red clay in NoVa I only grow vegetables in raised beds or pots. Tomatoes in self-watering pots, with cages. Cucumbers in raised beds, and pots, but my bets setup is a 2x8 raised bed on legs, with two A-frame trellises - that way I can get 6 plants in and a ton of cucumbers. Highly recommend trellises for cucumbers (or fence, wire shelves, whatever you can get them to climb on so the vine and fruit is off the ground.)

have you had success growing cucumbers or tomatoes directly in the ground vs. raised bed?

You can grow anything in a raised bed.

I like beds for toms. Last summer I also included cukes (using the fence as a trellis) and they took over the beds. So this year I will use pots for the cukes and continue with beds for the tomatoes.

I grew cukes in 5 gallon containers with tomato cages with additional stakes. It worked fine.

The tomatoes work in either the pots or a raised bed. I'd think the peas would do best in the raised bed.

Cukes I have a hard time seeing anywhere besides the ground, but I guess you could put them in a raised bed up against a wall or fence.

Should I plant tomato, cucumber and pea in a raised plastic bed garden (with 4 long legs) or in individual big plastic pots, which one makes more sense since I have to put in cage, trellis or sticks in them? And, which styles and materials are better, wire, cage, trellis or sticks AND wood, string, plastic or metal?