I did part of the section you're talking about - Labyrinth Canyon (put-in at Green River, UT / take-out at Mineral Bottom) - a few summers ago. It's a 68 mile float. It was exceptionally beautiful but flat as paint. A sea kayak would be a great choice and a canoe would be second. I wouldn't take a raft because you'd have to row the entire time, and if the winds picked up (which they do), you'd be hosed.
The camping is excellent, there are huge beaches (bring the bocce and horseshoes), nice side hikes and plenty of swiming. You will have to get a permit to float Labyrinth Canyon, which can be done in Green River, UT. We did the float in 6 days which was about right due to high winds that we battled every day.
If you float the 52 miles below Mineral Bottom through Stillwater Canyon, you have to be transported back up river via jet boat to Moab. Stillwater Canyon is in Canyonlands National Park so you have to get a permit from the NPS for that section.
For more specific info, check out http://www.blm.gov/utah/price/labyrinth.htm
Don't forget the beer and remember to LEAVE NO TRACE!