Peas like to sleep up high. Ours have a dog run for their "coop" that is 6 feet tall; they insist on sleeping on its roof in all weathers. That's really not a good idea, but our winters are mild enough that they've gotten away with it so far. If I were going to build them a coop, I'd make it at least 8 feet tall and put the perches up at 5 feet, or possibly a little higher, and I'd fix things so that they couldn't get onto the roof of the coop. They need to be protected from rain, snow, and wind, so having a coop that is enclosed on 3 sides and the roof is important; depending on how your winters are, you might want it enclosed on the 4th side as well. They need ventilation just like chickens do, so that's a consideration. Gates . . . ours have a chain-link fence for their yard, with an ordinary chain-link gate. Coming up off the chain link is a wall extension consisting of a 4-foot-tall strip of chicken wire, which is partly supported by 8-foot posts wired to the chain-link posts. We attached Top-Flight netting to the chicken wire to create a roof, and propped it up on more poles. Peas fly incredibly well, so roofing it was essential. The extra height lets them fly a bit, and it keeps the netting off of our heads. We haven't had any problems with peas trying to sneak out the gate when we open it, but it's not a bad idea to make it open inward just in case.
Where the chicken wire wall extension crosses the chain-link gate, we have one of the stupidest designs I've ever created; I call it the Facebreaker. Basically the chicken wire comes down and crosses the gate space at about 5 feet off the ground. At the time I thought it was a clever way to create a "flap" so that the peas couldn't squeeze out between the top of the gate and the bottom of the chicken wire. It wasn't; it was, however, a way to learn what it feels like to have your face pushed into a cheese-grater. So when you design your gate, put a lintel on it and attach your wire to that. Your nose will thank you.