I've been trying to imagine a cheap(ish) fencing option combining your requirements and it's not happening

Time/money and labour will not come together on this one!
For me, the real sticking-point is trying to incorporate chickens into your extensive system. Having to have a mesh fence to keep them in seems like a massive outlay. Or am I misunderstanding and the mesh serves other functions?
Maybe not attempt to fence them in at all? If they're getting scratch feed to keep them 'at home' and there's plenty of free-range, they will generally stick around. My parents have chickens in a coop and (massive) run which is pretty much always open into the paddocks. There's so much food nearby that I've never seen a bird bother an escape attempt.
I think the US and NZ tend to have pretty different fencing systems. We are BIG on electric fencing here and there's a broad range of good solar battery systems.
If you run a hot wire along the top of the permanent fence, there's lots of simple, easily moved strip grazing setups available.
It all takes a pretty serious outlay, setting up irrigation for stock not the least of it.
Joel Salatin has some good descriptions of setting up moveable water/shelter for rotational grazing.
Critter Caveat: I don't know your predators, but if they're a problem, a bit of fencing won't stop them!
I also don't know horses and I'm aware they have some specific vision/spooking/grazing/parasite issues.
I think barbed wire should be illegal. But with a bit of training, stock will quickly develop respect for an electric fence (Salatin has more on this. And yes, I think he could have many useful ideas for you).