Well, REI would be fine. They are professional and experienced. The only problem I have with the trip you linked is that they don't really say where they will be taking people. I assume they just want to keep their options open. It is apparent they are taking the north route out of Tuolumne Meadows, through the domes but other than that, who knows. If you decide on this option, it will be a good trip in great scenery. Be aware that although the trails in that area are not difficult, the elevation is not to be ignored. Tuolumne is pretty high at 8,600 feet and the trails go up from there. Be in condition.
Another outfit that you might want to consider is the excellent Southern Yosemite Mountain Guides, which has been featured several times on the TV show Motion. SYMG is probably the best in the business.
http://www.symg.com/