I place the stamps directly on the glass, then scan the entire platen at once. I then use the
StampFix app I wrote to extract the individual stamps from the scan, straighten, and crop. This way, the stamps don't have to be in any particular position or orientation on the scanner, like so:

To get a black background, I bought a sheet of
Strathmore Chromolux black from Hobby Lobby and attached it to my scanner lid with double-sided tape. It's not too matte, not too glossy, and gives a nice, consistent black background without the fibers you get with rougher construction papers or posterboard.
