Let's clarify terminology. Welded wire is sometimes called hardware cloth, although sometimes the term hardware cloth is used to refer to welded wire that has small openings between the horizontal and vertical wires (say, 1/2" by 1/2" for example). There's no real uniform standard for what you call welded wire products based upon wire spacing that I know of, though.
Welded wire is to be distinguished from woven wire (like chickenwire). Instead of welding the vertical and horizontal wires, the strands of woven wire are just twisted around each other, making the product less strong and secure.
Wire comes in different gauges, or thicknesses. The lower the gauge, the thicker and stronger the wire. Finally, welded wire can be galvanized (coated with zinc to prevent rusting) either before it's welded (GBW) or after it's welded (GAW). Wire that's galvanized after welding is stronger and more expensive, and it lasts longer.
Wire with openings no larger than 1/2" by 1/2" inch will stop "reach through" predation, so many people use wire with larger openings and just wrap the bottom 2 or 3 feet of the run with wire that has the smaller openings, or even with something solid. If you use wire with larger openings for the higher part of the run and/or the roof, be careful that the openings aren't so large that something like a weasel or a young raccoon could squeeze in, because they certainly can climb. However, if your chickens are going to be locked inside a secure coop at night when predator risk is highest, this becomes less of an issue.
