The chickens will be shut in the barn nights, and we have hardware cloth to bury an apron around that. We don't have dogs around here, so the chicken wire is pretty much to keep the chickens in, I think? Their run is pretty close to the house, maybe 10 yards out? So I wasn't worrying too much about predators other than birds for the run. We do have all the wildlife around, but I haven't seen then except at night, (fox, raccoons, opossums, etc.) We do also have 4 cats, which I think help some on keeping furry trespassers out. 
We have 4x4 posts on one side to fix the fence to, so we may need to put in a couple more on the other side for corner posts. Oh, that's another thing. We have 4x4 posts on one side because it is the pool fence, which is wood and I think about 6 foot high or so. Er... if the chickens got into the pool area, are they going to fall in and drown? 
How come green metal posts are called T-posts? They don't look like Ts! Okay, that's a bit off subject, but still..
I think we have enough posts to put them at most 5 foot apart, if not 4, so yay!
I was planning on affixing the 2x2s to the t-posts by bolting a 2x2 to the top of each post, and screwing the abutting 2x2 to the next bolted end. Does that make sense? I have a hard time explaining things without a pencil and paper. 
 So each 2x2 will have one end bolted to a post, and the other end screwed into the bolted end of the next 2x2. Does that sound alright?
I think we may have enough hardware cloth to bury an apron around the entire fence, but I thought that was pretty pointless since the chicken wire itself would give if something tried to get in?
I don't have anything around our veggie beds, and we don't generally have issues there, the only rabbits, moles, etc I usually see are in pieces 
 But I realize those aren't really the same as chicken predators. I have seen the cats run off foxes, raccoons, deer, and opossums before, but.. then again, I have also seen them all huddled in the porch growling at the fox outside the cat door, and also sitting quietly watching a HUGE coon eat the catfood out of their bowl IN the house without doing a thing. The thing was sitting 
right next to my feet while I was at the computer. Eventually something about the snarfing noise worked its way through my absent brain and I realized the noise I'd been hearing was 
not the way my cats eat, even at their most impolite. 
 It didn't care a lick about my being there OR the cats. (We have a 3 season back porch that has a cat door going into it. There is another door from there to the house that is usually shut, but sometimes in the summer when I was tired of opening the door every 2 seconds for 4 cats to go in and out I would leave it cracked... not so much anymore! Certainly not at night 
 One gets sick of coons and birds and small dead things that used to go "squeak" in the house.)