I'd definitely recommend doing the "A" Section first. They call that section the aquarium, when you see it you will understand. The river flows through a deep canyon that is probably 1,000 ft deep, it is just flat out gorgeous. The estimated fish count there is in the neighborhood of 10,000 fish/mile, it will mostly be rainbows, cutbows, cutthroat with a few browns. The "B" Section is just the reverse, mostly browns with a few rainbows thrown in. The wife will definitely enjoy the float. I can highly recommend James Boehm as a guide, he works for Old Moe Guide Service.
Guided Flyfishing trips Green River, Fly fishing the Green ,Green River Fly Fishing Outfitters River and Flaming Gorge, Utah Fly fishing guide Service