Pick up the "River Maps" guide for the San Juan. You'll be glad you did. You'll be fine on a 7-day permit, but push your first few days so you're not hating life below Slickhorn. Because of the sandbars, you'll be doing switchbacks across the river and a 15 mile day will actually feel like a 25 mile day. Be prepared to get stuck on rocks and bring a good patch kit.
As far as rapids, there is a debris fan just below John's Canyon that you should plan on getting stuck in - not to be pessimistic, but there just really isn't a channel through there at low water, although I got through at 480 cfs by moving sort of right of center to the center and kissing about 5 rocks on the way. Government is a little fucker at low water - scout on the left.
There are great camps all along that stretch. They are sort of sparse in the first canyon between Sand Island and Mexican Hat. Try to do the Mendenhall or Honaker hikes, and aim for a slickhorn camp if you can. Have fun!
“May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view. May your mountains rise into and above the clouds.”-Ed Abbey