I highly recommend talking with Trevor, Gabe and Venture Vans. My family had a wonderful experience with 6 nights of camping/touring Jackson Hole, the Grand Tetons and Yellowstone.
The Mercedes-Sprinter--Sportsmobile-Camper van was easy to drive, maneuver and most of all, it was great way to see the parks. We could go anywhere and still have our food, 'lodging', space, privacy, etc. Once you get used to working with the seat belt straps on the bench (which folds down to become part of the bed), setting up for 'nighttime' was a simple process - just a few minutes to prep the van, and a few more minutes to put the bedding down. Our two boys (12, 9) slept in the 'pop-top' (they loved it!) and my wife and I were in an awesome double-person sleeping bag. Having a fridge and stove top enabled us to stock up on groceries (reducing travel costs) and we cooked most lunches/dinners in the van - and had simple breakfast foods in the morning. Having such a great 'hotel on wheels' enabled us to focus on the fun stuff...being with family in an awesome part of the country. On only 1 night of the 6 , we were plugged into water/electrical - and on the other 5 nights, we only put a dent in the amount of available 'tank water'. The gray water (sink drainage) was easy to empty and the small portable toilet was very handy to use and kept us from having to leave the van, in bear-country, to do our thing in the middle of the night. The fact that there were solar panels to recharge the electrical system was awesome too...our phones and tablets stayed fully charged the whole time (although we didn't always have service in the parks).
If you do rent, give your self some time to review all of the features of the van when you pick it up. I'd recommend packing a headlamp for each person as well as warm clothes - we were in Yellowstone in late May and there was 2-3 ft of snow in our campground. The 'pop-top' might be chillier at night (canvas sides), but my boys didn't bat an eye. Advice on suitcases - if you are 2-3 people, you can probably get away with hard-cased bags...but in our case, and this was our 3rd similar trip with a camper van (OR & AK were the others), so we've learned to pack clothes/gear in canvas-style bags...bags that can smoosh into spaces that hard suitcases cannot. For each night/morning, there is a transition - bedding, bags, etc - have to be moved to create space for sitting - and a side note, when camping in Yellowstone, you cannot leave any items (except for chairs, wood) in the campsite...everything must return to the van. There is ample storage if you use the space accordingly - for instance, my wife and I each put our duffel bag on a front seat during the night - we had access as needed. Those bags transitioned to the back-under-storage while driving. We quickly developed a routine and if you rent it, I'm sure you'd do the same. Easy, simple.