The pieces would be ~1-2 inches long, .5-1 inch wide, and .25-.5 tall. there would be 30-40 pieces. What about tiles that would be 1/8-3/16 tall and 3"x3"? I would prefer if the materials came in different colors.
Might need a little more information…
Plywood and MDF are very cheap, come in sheets of many sizes and widths and can hold pretty good detail. I made a functioning wooden clock out of ply, including the gears etc with no problems at all. MDF can take reasonable fine detail and has no ‘grain’ to worry about.
Have a look at the materials list here in the Inventables site, it’s got a pretty extensive list and many of the items have a little bit of an explanation about what they’re good for.
If you describe what you’re making (chess pieces, scrabble tiles etc) I’m sure you’ll get some great suggestions.
The closest analogy would be meeples and carcassonne tiles.