On what can I mosaic?

I'd like to add character to my family room by making a mosaic tray
that fits perfectly on a 16" diameter round accent table, turning it
into a tray table of sorts. What kind of surface would be good to put
a mosaic on? I do not want to mosaic the table itself.

Generally, I get the impression that whatever I put a mosaic on should
be unbending (or else the grout will break and pieces will fall out)
and resist water.

The obvious choice is wood, but I'm finding wooden 16" circular
serving trays to be hard to find in the inexpensive don't-feel-guilty-
about-painting-it variety (I'd like it to be white and could paint it
if it isn't - do you know of any sources for economical paintable
wooden circular trays?). I also might do the same thing for a round
24" table too. I'm concerned that metal trays may be so thin they'll
bend and make the grout fail. Melamine is definitely out. Do you have
any out-of-the-box ideas for me, or should I just keep trying to find
a wooden circular tray I can paint?

Here are some ideas I've had. If you can comment on them, that would
be great.
- Find a round picture frame and mount it on something like cement
backer board (like wonderboard) or mdf. (It hasn't been easy to find
affordable round picture frames. Sources, anyone?)
- Get a disk of mdf or wonderboard, screw in a couple of handles, and
mosaic that. I'm not sure I can make a raised edge kind of tray like
that, though.

Thanks for your remarks,
JeanneP