Now we're getting somewhere. Sandwhich the thin stock between two pieces of thicker stock. Wood will work but to really keep the thin plate stock from lifting/burring at all when the drill flutes get a bite on it, I'd use scrap metal (steel or alum) and really pinch the plate tightly.
Also firmly secure the work to your drill press table, forget about the bench vise and the hand drill. If the work is not firmly secured and drilled with a rigid spindle (as opposed to hand drill), the thinner the stock is the more likely you end up with a "triangular" (also under sized) instead of perfectly round hole.
This is the sort of drilling operation that a mill is real handy for but there's no reason you can't do just as well with a drill press, it will just take longer to set up.
Dennis van Dam