Anything with a vertical bobbin and a largish harp. Model 15s come up a lot as being very good. They're extremely plentiful too, so they're usually "cheap".
Hey Candace,
Have you tried anything free motion by setting the stitch length to 0 instead of raising the plate? I haven't yet, but the book goes into detail about FM embroidery, etc, you'd think it should be possible.. .