The larger the inlay, the thicker I like it. I use .03 for small inlays, 1 x1 or so. For bigger inlays, say 1x 2, I use .04.
Hoover and Strong for silver and gold sheet. Rio Grande, too. I'll bet you could get some sheet from Track of the Wolf, Dixie, or MBS and the like.
Old coins are a good source. Silverware.