For costume maille, the best ring size depends on what is most important to you- speed of manufacture, weight, appearance, sound, sturdiness, or price.
For manufacturing speed, .10" (2.5 mm) x 7/16 to 1/2" (11-12 mm) ID aluminum rings would probably be fastest, but it is going to look really, really big. .08" (2 mm) x 3/8 ID is the biggest I would personally use.
For weight, aluminum about 1/3 the weight of steel. I made a short-sleeved knee-length .08" x 3/8" ID stainless steel shirt, which weighs 35 lb and has around 16,500 rings. (I'm about 5'-10", 190 lb.) Scaling the ring size by half would halve the weight, but would quadruple the number of rings required.
For appearance, aluminum can be shiny, matte, or anodized in various colors (before weaving). Galvanized steel will be dull, and will darken as the zinc coating oxidizes. Stainless steel will pretty much be forever shiny.
Sound is one of things you may not think about, but there is a distinct sound to steel maille that aluminum and titanium do not have.
For sturdy maille that will not shed rings as you wear it, I would suggest an aspect ratio (AR = ring ID / wire diameter) between 4 and 5. For aluminum, I would try to keep the AR closer to 4, while 5 would be fine for stainless). The minimum possible AR for a European 4-in-1 weave is in the lower 3's, but shirts require tailoring, and therefore expansions and contractions in the weave - an AR of 4 is about as low as you would want to go for tailored items.
Price - I don't know what's cheapest, but I do know that if you buy your own wire, make sure that it is tempered. When I started mailling, I bought wire that was too soft and was useless. My first shirt was made with galvanized wire that I coiled and cut by hand, and I shall never, ever, do that again. I now get my armor rings from theringlord.com.