Best time of year is when you want to go, depends on your weather and crowd preferences. Summer six months expect hot and crawling with people, winter is cold and lasts well into spring, but the canyon is at its most beautiful when covered with snow.
My own preference is September and October, for most all of the western Colorado Plateau, not just Grand Canyon NP, but I have friends from Alaska who prefer to visit GC November through January.
The best place to stay is one of the resorts on the property. If you must stay in your RV, Trailer Village is most convenient for access to public transport on the South Rim, but it is a rather tight RV parking lot kind of location, not a campground experience.