Where can I get a chalkboard?

Since many school districts are in the process of closing down schools to save on budget costs, you might be able to find some used chalkboards at your neighborhood school district office. If they don't have any, they can probably point you to another source.

Other than that, a Google search for 4 x 6 chalkboards brings up chalkboards for sale at around $200.

chalkboard paint is the way to go. I've used it several times although years ago. I'm struggling to rember but i think we used a priming paint to seal the bare wood then 4 coats of blackboard (chalkboard) paint.

Interesting that you thought the profeesionally made board "expensive" yet the do it yourself version was labled "cheap"
edit: the timber we used was masonite ( a fine partical compressed board) which has a smoothe side and a rough side. We painted the smooth side so no need for primer.

Interesting that this received a "math" tag because of plans "to do some fairly heavy duty math on" the chalkboard.