I also definitely recommend taking the Red Bus tour - well worth the money, IMO. We took the all-day roundtrip one that covers much of both east and west sides of the park. I second (third?) the opinion that going to southern Utah first and Glacier afterwards is a good one. Some years, Going to the Sun Road isn't even open until mid-July, depending on the snowpack and how cool the early summer is.
There are a lot of decent CGs just outside the park on both east and west sides; check for CG reviews to see what you would like. If you want wooded sites, Mountain Meadows is good for the west side; if you want more space for a large RV and satellite TV at night, the West Glacier KOA is very nice. All the CGs inside the park are no-hookups, and IMO weren't heavily forested. Lots of pull-throughs and we did see some bigger rigs in there.