First off I'll say you will love it. Amazingly spectacular.
I camped mostly - started in Two Medicine campground which is spectacular. It's on the East side (the more rugged side). I think we also stayed at Many Glacier campground but I can't remember. Finally after we did the Going to the Sun road we stayed a couple days in Apgar campground.
A note on camping - due to bear activity they are hyper paranoid about any food or soaps, etc left out. You'll be fined if they find any at your site when you aren't actively using it. When cooking dinner the camp ranger came to us to give us the bear warning even though we'd heard it repeatedly. You can't dump any cleaning water or anything with a scent (the bottom of a beer or soda) out at your site. It all has to go to dump stations.
We also stayed in a motel for a night or two to get a good shower. Wasn't affiliated with the park.
We hiked up to the scenic point over the Two Medicine entrance to the park. Great but long hike. The best hike was Iceberg Lake Trail - on the East side and I think it leaves out of Swiftcurrent. We did a guided (ranger) hike because it is (or was) the most grizzly intense area of the park. There had been a bear on the trail everyday of the week when we went (we fortunately avoided). Probably a group of about 15 people. Was fantastic. The first picture below is where it ends.
The lodges are worth visiting even if you aren't staying there.
You have to do Going to the Sun road; maybe more than once if you can swing it. When I was there in the 90s you could drive pretty freely on it but I thought I've heard traffic has been restricted and maybe you'll have to do the Jammer bus.
Everywhere you look is spectacular - hard to go wrong with anything you do there.
Agree with advice about clothing - weather changes like crazy. Another thing is that if you are there in mid-summer be prepared for very long days - I think it stayed light out to almost 11pm when I was there.
Some day I'll go back.
Iceberg Lake - this is the termination; right at the Continental Divide. That wall of rock will blow you away when you see how big it is compared to how it looks in pictures.