Welcome!

I wouldn't bother with advance booking unless you want to stay in the national parks themselves or have a desire to stay in a particular hotel at a particular time. Anywhere else, you can generally find a walk-in unless there is a special event going on in the area.

I would use all 3 methods as needed to keep your trip sorted out. Just don't overplan so you can be spontaneous if something catches your eye. This is also why you shouldn't (in my opinion) book everything in advance.