Coins To Use As Decoration

A low grade 1840-1856 Large Cent would be a great conversation piece. Dates prior to 1840 and the 1857 would cost over your budget.

Worn but legible Indian Head cents can be bought wholesale for ~ $1 each.

If size matters, large British bronze pennies are even cheaper: 50c. to a buck in quantity. Also the last year of those, 1967, is often available BU.

Modern foreign coins of wide variety are plentiful and cheap.
Seems like the choice of coin might depend on the context in which it is going to be used. Keep in mind that coins in contact with other materials such as wood boxes will likely corrode over time if not protected.

To help narrow down the choices, is the size important? And how about the color (copper vs. silver, as you're probably not considering gold for this project)?

We could probably give better suggestions with an idea of what you are going to be making. I'd second using a world silver coin; you can get plenty of nice, large silver coins for cheap since silver prices are down right now.

Maybe one of these?

Thanks for the input everyone! I'd like to have something between quarter and half dollar size. Preferably silver or silver colored. Specifically I'm thinking of embedding them into simple wooden ring boxes, maybe using a clear epoxy to cover.

I like that! Half-dollar size would probably be best -- a dollar might be too large, and you'll lose the impact of the wood box (the coin will be too close to the edge, so you'd mainly see the wood only on the corners).