Ian, your request is pretty hard to reply to--there are so many considerations here. My advice is for you to buy Erik Molvar's Falcon guide book, read it, then come back to us with specific questions. However, here are some thoughts:
Early July isn't the best time to be in GNP, really. Several great places aren't accessible that early, due to snow pack. For instance, the Northern Boundary trail, the Garden Wall, and Gunsight Pass. The bugs (mossies and flies) can be fairly nasty then too, but manageable. The nice thing about July is the amount of daylight you would have. It doesn't really get dark until maybe after 10 PM, due to being that far north around the summer solstice. Weather is hard to predict. You likely will have highs of 65-80*F, and lows of 35-50*F. There isn't really a sort of monsoon season in Glacier, but you could get socked in for a week of rainy weather (not likely, though). The area that melts out soonest is the Belly River in the north, and perhaps the lower elevation forested lakes in the west--Kintla, Bowman, and Logging lakes (if there isn't a heavy snow pack that year, which would be slow to melt along the shaded trails)
You will each want to carry a personal can of pepper spray for griz deterrant. You can't fly with these, so you'll buy them there, then drop them off at a permit office or visitor center when you leave, so that someone else can maybe use them. The backcountry rangers like when you do that--free bear spray for them, and they'll certainly use it. Be sure to watch the bear video when you get there, even if you don't do any backpacking. You need to get educated on how to act if you meet a bear. The beautiful Many Glacier area is a major haunt for griz, and they use those trails too. Always carry your spray, everywhere you go. Learn how to use it. And don't believe the common addage, "You won't see a griz on this trail--there are too many people hiking on it." My only true face-to-face griz encounter happened 2 years ago while hiking to Iceberg Lake, when 150 others were also hiking there. Also, BPL member Rob Kelly and his mates saw one at quite close range when they did a day hike along the popular Garden Wall last September. And watch out for any moose you see. Keep an eye on them as you pass them, give them a wide berth, and don't stop at close range to pop a lot of photos. You just don't know what they'll do, and they can get pretty goofy if they feel you're invading their space. They're a lot bigger than you are, and they can deliver a world of hurt if they're mad at you. Mothers with babies are the most dangerous, just like a bear with cubs.
There's almost no way to avoid the crowds in GNP during July and August, especially on day hikes. You won't see a lot of folks on the trail when backpacking, but you will share campsites with others. Each party will have its own tent site, but you share the food prep area, the bear food pole, and the outhouse/privy. Car camping sites in/near the Park fill up fast, but the ones at the western lakes don't see much demand. I don't fish, but you might be able catch some at those lakes.
Backcountry campsites reservations can be hard to score. The best thing to do is to apply for those now, and get in line for the lottery drawing in April-May. Then, if you don't get what you want, try to score them once you arrive. Half of the slots at each campsite are held until 24 hours in advance of the trip, but these also are quite competitive. You'll need to get to a backcountry office before 7 AM to try that.
I'm sure others will offer better advice than this. But buy that book, and then come back with specific questions. We'll try to help.