I followed a lot of route 66 this past winter. Some of it is so badly deteriorated that driving on it will scare you. Some of it goes right through the middle of little towns and becomes a narrow street with parking on both sides and stoplights. It crosses and/or blends with route 40 in many places. The best stretch that I was on went through Williams, AZ.
I doubt that you will need any reservations unless there's a holiday or a special event going on. Of course, in major population areas, arriving on a weekend may necessitate reservations.
Frankly, I was pretty disappointed in route 66 and really thought that, given its history and historical importance, it would be better preserved. Some maps show it as the National Highway, others don't show it at all, even though it's still there. None of the maps I have show it as route 66.
The route 66 website was a big help.