Once you get past the beginner stage, you will be encountering very turbulent water. In addition, many rapids are formed in shallow spots and it is no fun getting banged up by rocks. Whitewater vests help keep you on the river surface and provide some limited protection when banging into rocks. At the same time, good vests shouldn't restrict your mobility. Most paddlers go with some form of Type III PFD specifically designed for whitewater boating.
One of the most important considerations is the right fit. This can be a significant problem for children and small adults. If the PFD is too large, it will ride up on the body and block your vision. In some cases, it may slip off the body during a rescue. Many PFDs come with adjustment straps to ensure a more snug fit - learn how to properly secure your model.
All PFDs must have very sturdy shoulder straps as a common rescue technique is pulling on the shoulder strap. They should be strong enough to lift a couple of hundred pounds in dead weight.
A PFD should be a bright color and ideally have reflective material. Pocket/s are very valuable on a PFD as well. I also recommend tie-downs and small loops for securing items like your safety whistle and river knife. I highly recommend ensuring your PFD is Coast Guard approved - some parks out West require this (like the Grand Canyon for instance).
It doesn't hurt to verify that it still has adequate flotation each year by jumping in the water. If it fails to float you properly (like it did when it was brand new), replace it immediately.
Later on in your paddling hobby, you may wish to upgrade to a rescue vest (after taking the Swift Water Rescue class).
If you have a choice, I highly recommend getting a PFD that has a strong front zipper. These usually have extra fasteners as well. Zippered PFDs are far easier to get in and out of and will not wreck zippers on your dry suit (spoken from personal experience).
There are a number excellent brands of PFDs available such as Astral, Extrasport, Stohlquist, Kokatat, NRS, and Patagonia (Lotus Designs). Prices range from $50 - $210 new.