<<Disclaimer: Verify this information before applying it to your situation.>>

Thanks to everyone who responded to my inquiry!  Very helpful stuff!
General tips were to make sure of the following:
Get a machine that makes at least 2 pound loaf
Get a machine that makes a horizontal loaf.
Be sure to get a machine that is programmable.

The ones people recommended were Red Starr, Zojirushi, Kitchen Pro from
Regal, Breadman, Welbilt,.


Some others also had interesting comments
 "...I know there is a whole page devoted to good GF bread machines on the
Celiac list website.  I looked at it once. The power of the mixer seems to
be the key."

"I would highly recommend using your breadmaker to mix the dough, and then
taking it out and letting it rise in the pan you'll bake it in in the oven."

"...since Gluten/Free breads do not have gluten, the second kneading and
second rising does nothing to enhance our bread."

"GOOD gluten free breads should mix and rise only once and then bake."