You don't indicate if you are planning to float most of the river, camping as you go, or fly in and set up camp in one spot for your entire stay. Both alternatives are possible, and it looks to me like week long camps on the lower river are the most popular.
I floated from the upper river (Giants) last summer, spending two nights at each camp we made. (It's not a very long float for 8 days.) The folks at West Coast Helicopter keep track of every party they fly in, and they will drop you off at a vacant camp site if you're floating. We never saw the floaters who began before us or came after us, only the guide boats that operate in the area we were floating through. There are plenty of people on the river, but we all seemed to be spread out. The rapids on the upper river are longer and more intimidating than I expected, but they are navigable.
There are fresh steelhead from the beginning in June, but high flows can mean few fish above the canyon. Flows should be more favorable from early to mid-July onward. You can catch steelhead all through the season, but July and August seem to be most popular.
Itinerary: go slow, take your time. If you expect to float 6 or 8 miles each day and set up camp, you will run out of river before you run out of week. The hardest thing for the week long float is not going over the helo weight limit. We took Scotch and wine, but the summer weather was perfect for a few cases of beer. That wasn't possible for 3 guys at 200# each.