What is the best plastic to make a see through 'whiteboard' with?
Markee Dry-Erase Paint is clear, so it won't even look like you've got a dry erase surface at all. You may want to put up an outline though, since I could see running off the edge of the painted surface being a problem. It's also a bit pricey, at $59/quart or $127/gal. (I haven't used this product myself, so no guarantees on how well it works.)

Another option is Opti-White dry erase film, also in clear. It's $26/ft for a 5' wide sheet. (So a 3'x5' sheet will run you $78 - it would be cheaper to go with the paint-on option, unless you don't want to deal with the mess.)

If you want to go the 'board' route instead of a wall covering, you could try Lexan. It's fairly lightweight and you should be able to get it at most home improvement stores. Lowes has it for about $70 for a 3'x4' sheet.