Go with a well established commercial outfitter. For the Grand Canyon section all of the companies must be certified by the National Park Service and as such must meet rather strict criteria for safety and experience. Any of the outfitters would be good.

Some operate giant motorized inflatables. This is certainly safe and comfortable, but I personally would rather be on a trip with paddle-rafts or oared boats to get the true river experience. There are many companies to choose from, start by looking here:

FourCornersRafting.com