It seems like most people use hardware cloth for the wiring. It's galvanized, which means zinc-coated, and some people say you shouldn't use it because of toxicity issues. But I looked into the issue before I built my aviary, and found sources saying that they haven't had any problems with it. BUT you have to scrub it in advance with vinegar using a wire brush to get rid of loose zinc powder. I ended up using hardware cloth for my aviary and the zinc dust on it was nasty before I washed it. Ordinary hardware cloth is the cheapest and easiest wire to find, and half-inch spacing is good for cockatiels. However my birds don't live in the aviary all the time so they aren't constantly exposed to it.
This thread has some useful info from long-time users:
http://board.birdchannel.com/Topic196870.aspxThe alternatives to hardware cloth are after-welded wire (aka galvanized after weld) which looks similar to hardware cloth. It's more expensive than regular hardware cloth but is said to have less zinc on it.
Other options are stainless steel wire, which is super expensive and hard to find. And wire that's powder coated or vinyl coated. NOT the flimsy vinyl coated wire they sell at Home Depot, but a vinyl coating that's similar to powder coating. Someone on the NCS board recommended this:
http://www.twpinc.com/wire-mesh/TWPCAT_ ... 10W48T-GRN It's good stuff, and it's $260 for a roll that's 100 feet long and 48 inches wide. I don't know whether shipping is extra. The price fluctuates up and down on Amazon and right now the price seems kind of high, but at the moment a same-sized roll of regular hardware cloth is $100 less with free shipping. Amazon has shorter rolls if you don't need that much, but it looks like the poly coated roll is only available in that one size. You might be able to find smaller sizes from other vendors.
Do you know what kind of wire the old aviary has? It's most likely plain old galvanized chicken wire, the same kind of wire that regular hardware cloth is made of.