I hiked it a few years ago over Labor Day weekend and it was great! We took the shuttle up to Chamberlain Ranch and hiked in from the top. Definitely a hiking stick or trekking poles, definitely a trash bag or dry bags in the pack. We had to swim a couple of sections in Sept. I would also recommend some sort of water proof camera case, every turn is another photo.
Also, I am not sure if they have changed the permit system, but when I did it, you had to be there in person the day before to register/pick up your permit. We got in line at 5:30 am outside the ranger station and were second in line, the folks who showed up closer to when the office opens got shut out. Granted we were there over a holiday weekend, but it would be a bummer to drive all the way down there and not get to go..
We hiked in shorts and Chacos and it worked out fine, it was over 100 degrees that day, but if I went back I would prob look into renting some Canyoneering shoes or at least wear some good river booties, just to prevent all the stubbed toes on the rocks you can't see.
Such a great hike, can't wait to do it again!