What type of campground is there?

They have rv camping and tent camping

Here's the park's webpage with camping info: https://www.nps.gov/grsa/planyourvisit/camping.htm

You actually can camp in the dunes with a back country permit. 20 permits are issued per day so get there early. Go to the visitor center to inquire about a permit.

You can't camp on the Dunes. However there is a camp ground off the Dunes about a half mile to the south. Just for safety reasons.