So you're talking about a modular board system?
Will you just paint on landscape, or stick on a printed tile? Or will you be making 3D terrain?
If paper/paint, you can use thick grey cardboard, and glue some black paper on the backside and your prints/paints on the top, and then varnish with spray. Pins can be stuck through.
If 3D terrain, I'd suggest 5mm wood or even 10mm wood. Easier to make pegholes in for toothpicks with a drill, not pins though.
Or you can make them from polystyrene. Light, cheap, but be carefull what paints/sprays you use. See more on that here.