We live in Utah and usually go to Yellowstone at least once a year -- more often if we can get there. We've only camped once in the last 15 years, but plan on camping in the future since we just bought a used Flagstaff 625D.
One thing that people don't realize about Yellowstone is just how big it is. You can spend an awful lot of time and gas driving around the park. Are you planning on including Grand Teton in your trip? If so, I'd recommended spending a couple of nights at a campground in Grand Teton (I'm partial to Colter Bay), and then relocating to Yellowstone. Depending on what you're most interested in doing, I might even try two different campground in Yellowstone.
Our primary emphasis tends to be wildlife watching, so I'm thinking of staying at either Canyon or Mammoth so that we're close to the Lamar Valley. If you're more interested in geysers, either Grand or Norris might be better for you.