Since your post suggested that you can go in July or in the Fall, I'd recommend the Fall for a 'little' less crowds and wonderful temps. If you change the time perhaps you can get a site in the park at Trailer Village. That's the ideal place to experience the canyon. The free shuttle stops right at the RV park and you can get on and off whenever you want. . . hike a little on the easy Rim Trail and hop back on the shuttle and repeat.
By taking the train you'll only have a few hours at the canyon. I know Dick B says it's plenty but we highly disagree.