We use several different things, but mostly welded wire. Lately, we have been ordering a lot of our wire through Ace Hardware because you can have it delivered for pick up at the nearest store, saving you the shipping which can be over a $100 for even one roll of wire.
The size and height you use just depends on so many factors. The smaller the pens, the smaller the opening need to be so that something can't reach through. If they are not covered, the fence needs to be taller. If you are doing raised cages, probably lower is better. If you want to be able to walk inside, again probably higher is better. It just depends on so many factors. I tend to like the smallest openings and the lowest gauge we can afford. Right now, I don't have any cages or runs with higher than 1 x 2 openings. To me, unless you are fencing a huge area like for a perimeter fence, the cost of the smaller openings is worth it. I have used 2 x 3 and 2 x 4 in the past and just didn't like it, unless for framed out perimeter fencing.
We, of course, have used some hot wire as well. We don't currently use any electric netting or even gamebird netting (although we have in the past, most of our cages now have welded wire roofs). We also never use chicken wire, it is just not sturdy enough. On occasion, for our larger birds' moveable pens, we use hog panels. Clearly though, you can't use those for permanent caging with no other sources of protection.
Anyway, my top pick for wire 36" inches and taller is the 16 gauge, 1 x 2 wire and my top pick for shorter than that would be the 16 gauge 1 x 1 or 1/2 x 1. For raised cages or cages small enough for something to reach inside and grab a bird, I prefer 1/2 x 1/2.
