It's going to depend on your preferences. Get on the search engines and read more about the parks that interest you then create your itinerary based on features you like.
Option: You can start out in Utah June 1 and see some of the sights along your way to Montana and Glacier National Park. We prefer Montana and GNP so we stay there longer. The glacier is indeed getting smaller and I would rather see that before it's completely gone. Then again after this year's frigid winter, it may get larger. Who knows?