The wire used to enclose the aviaries is NOT fencing. The fencing materials you'd buy at places like Home Depot etc. first of all is too large to use. It may keep your birds in, but it won't keep other critters out! You need to be cognizant of wild animals (raccoons have been known to injure/kill birds), rodents (can easily slip through that standard fencing).
I think Lori used the standard carport cover frame that you can get at Costco. Actually, I'm building some aviaries now using these.
If the aviary is to be built on grass/lawn/ground, I'd suggest wiring in the floor as well, so that the critters mentioned above cannot dig under to get into the cage.
You don't want to use anything larger than 1/2" x 3" wire. The gauge you'll want should be heavier as well, especially if the enclosure is to house larger hookbills (greys on up...including cockatoos--other gauge wire might be too easy for them to destroy), so I'd say 12 ga wire would be what you need.
You'll want to order GAW (galvanized after weld) aviary wire. You'll want to make sure you wash it well in vinegar and water and rinse well before you put your birds into it. This will loosen/remove any zinc particles/residue (which you don't want your birds to ingest).
http://www.naturalbird.com/faq/
http://www.sierrawireandsteel.com/index_cages.html
If it's in your budget, there is stainless steel wire:
http://www.twpinc.com/twp/jsp/product.j ... oardId=112