Step 1: Choosing Your Materials
The first step is to decide what kind of metal to make your shirt out of. In reality you only have 4 reasonable options. They are pictured below. To learn more about the materials, go to Chainmail Wire Types. Don't buy anything yet though. The amount of wire/rings you will need depends on what kind of shirt you are making.
Mild steel is affordable, strong, and very realistic looking. However, the downfall is that it does rust. If you choose mild steel, keep in mind that you will have to keep it oiled to prevent it from become a pile of aluminum oxide.
Galvanized is virtually identical to mild steel in terms of cost and strength, but it has the added bonus that is doesn't rust! It has a zinc coating that prevent the steel underneath from oxidizing. Some people don't like it because they are worried about zinc poisoning, but their fear is unfounded. The only way zinc is dangerous is through inhalation of the fumes it lets off when it is heated up. Which shouldn't happen, unless you are saw cutting the rings.
Aluminum (14 gauge)
Aluminum is cheap, shiny, and very nice to work with. The only drawback is its strength. You either have to use really small rings, or a really thick wire gauge. Or both.
Stainless steel is stronger than mild or galvanized steel, and is also very shiny. However, stainless steel is more expensive to buy.
There are other materials to use, listed under Chainmail Wire Types, but they are either expensive or too weak to use.