We use a booking agent, although going direct to an outfitter is perfectly acceptable. I use Wendell Reich at Hunter's Quest International in Dallas.
Using a booking agent is well worth the effort. They can smooth over the inevitable rough spots, be it recommending a quality outfitter, booking the hunt, assisting in obtaining permits, and assisting in trophy shipment and other things that will crop up. An agent can also set you up with good side trips to various parks and other interesting destinations.
I also use a travel agent for the airline bookings. This is very valuable in case of a schedule change or unforseen events, like flight cancellations. Most good ones, like Gracy Travel, have 24 hour phone service and great internet service, as well.
Using a booking agent and a travel agent takes a lot of the uncertainity away. We're booking another hunt with Wendell in 2011 and will continue to use him for the forseeable future. We're booking travel through Gracy, as well.