The link above didn't work for me...and perhaps not you, but here is the official Yellowstone Nat'l Park site with all their campground information:
Yellowstone Nat'l Park CampsitesWe've never made reservations for Yellowstone but you need to be at the campground early morning and yes, Mammoth is our favorite. However, with your small rig you'll have many more wonderful choices. You might even considering moving to 2-3 different campgrounds within Yellowstone for varied experiences and perhaps different critters. Have fun!