If you just want something cheap and small look in the toy aisle at the Dollar Store. It's only a dollar.
I have a dollar store set in my office at work. The board that came with it was some type of folded plasticized paper that would never lose its creases. The pieces would never stand up near the creases. I just looked around and couldn't find the board. No big loss. It's easy enough to print a board on regular paper.
That may be the cheapest way to get a workable travel set and sure beats gnawing pieces out of rocks.
If you just want something cheap and small look in the toy aisle at the Dollar Store. It's only a dollar. If you don't like it then give it to a kid. You may spark an interest. I carry a couple of those sets around in my bag for analysis and odd bored moments.
For a "real" travel set I have a set made in Jerusalem from olive wood. That set costs in the fifty dollar ballpark. Drueke makes a travel set for around twenty dollars. The pieces are hard to distinguish so I don't use it much.