Wow, there are probably as many suggestions as there are people. The smaller the opening in the wire the better. And the thicker the wire, the better, so no chicken wire. Chicken wire keeps chickens in, but does keep predators out.
If you are asking about hardware cloth, it is basically just wire with about a 1/4-3/8 weave. They use it quiet often for eave and foundation vent covers. You can buy it at most any hardware store. But it won't be cheap. The advantage is that it is tough and small, so no paws can get through it.
You can use chainlink, but it is easily climbed, and critters can get their paws through it. It your run has a top on it then clilmbing is not an issue, and you could use chain link or no climb wire and put a smaller guage wire around the bottom 2 feet or so. That way raccoons, etc will have a hard time reaching their paws through it. If you use a welded type wire that an animal can get a paw in they can then work at it and sometimes break the weld on the wire and come on in. Do you understand the difference between welded wire and field fencing type wire? Most feed stores can show you the difference. Again, price plays a big roll in choices.
Personally, I have used the plastic chicken wire looking mesh over field fencing. I also have it inside my goat pasture and both the run and the pasture have an electric fence around it, so that helps a little. I am planning a cement floor soon. That way no one can dig under. I am also planning on replacing my plastic mesh with hardware cloth or rabbit cage type wire as the budget allows.
Feed stores usually have the best selection of wire. Hope that helps.
