Be sure to check the park on-line calendars to make sure you can do what you want to do. Portions of Glacier NP close up early, after Labour Day.
This page is really helpful: https://home.nps.gov/applications/gl...s/cgstatus.cfm
If you're going to Glacier and Banff, think about Waterton Lakes NP in Alberta, as well.
We've camped at both Fish Creek and St. Mary in the park, which are fairly standard Park Service sites: no hook ups, parking pad, picnic table, fire ring. We've also stayed at the commercial Glacier Campground in West Glacier. Not luxurious, but nice vegetation screening between sites.
If the road is still open, we really recommend the drive up to Bowman and Kintla Lakes. This is a rough road, but the scenery is super and you lose most of the other people.