Good description by wyosam and yes, you want that waist strap & buckle. One thing to bear in mind is that lots of folks get mixed up with PFD designations and call them "class 3" when it should be "Type 3" etc.
The low-profile PFDs you normally see kayakers and many rafters wearing are Type 3 and usually have about 16 - 18 lbs floatation, the more bulky ones with the big pillow on the neck that you see commercial customers typically wearing are Type 5 and generally have about 25 lbs floatation. These PFD designations don't have anything to do with what "Class" the whitewater is ("Class III," "Class IV," etc.).
Whatever you get, be sure to read the label in the PFD and make sure it's for whitewater, or that it doesn't state that it's NOT for whitewater paddling use. Those are things the rangers will look at when you check in on permit runs.
Good luck shopping!
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse