Ive never done a shirt but i wss asked to help do just this costume for halloween last year....
Aluminum sounds like the winner if you want a full shirt. Its a third of the weight of steel and you get twice as many rings for the same price at 16g 5/16.
Alternatively you could do a little cosplay trickery that this guy ended up doing and not even do a full maille shirt. If you're basing it off the movie you can only see the maille shirt's sleeves and bottom hem area from underneath the side dags of the leather smock.
To really save on weight and cost start with the leather parts of the costume and then weave just the parts of the maille that you can see plus a couple inches and stitch them into the inside of the leather smock. If you go this route I'd use some welded stainless rings for the attachment points so they don't open or let your stitching material through the kerf.
This would save quite a bit of coin, weight, and a SUBSTANTIAL amount of your time. We chose this route because he came up with the costume idea about 8 weeks before halloween. Not enough time for a full shirt. And the time was better spent getting the rest of the costume looking good anyways.
He ended up choosing stainless for a couple reasons. We had the wire on hand. It just "sounds" better than aluminum when you move. Stainless won't corrode. Once he got the sleeves and hem pieces woven it was determined they were too shiny. We hung them up by some wire and use a propane torch to give them a richer earthy bronzish color which turned out great. Then we cut out some chunks around the edges wrapped around a log an took glancing blows with a sledgehammer to deform some of the rings (repair opened rings after each blow... trust me). After everything was said and done it looked like a piece of battle worn dress.