We have done the fly-in-and-rent thing, several times. Being from Europe, there is little choice... We twice rented Class C campers in the US (Cruise America and Moturis/Camping World) and once a truck camper in Canada (Fraserway). We have actually been to the Grand Canyon on two of the trips, so I feel somewhat qualified to respond ;-)
Our experiences were good with all three companies and rentals, but there was a clear ranking.
In my opinion, one week is quite short for that sort of trip.
Some thoughts:
- The pickup/return time and location of the rental may not be very convenient with relation to your flight/airport. Even the major players are pretty far off the airport and you need to take their shuttle out to their location and back. Some rental companies have rather restrictive pickup/return times, too. You can figure that you will lose at least the complete first and last days of your trip in the process.
- While you can rent bedsheets, tableware and so on with the camper, you will still need to bring or buy any food items. And, of course, your personal belongings. It can be quite time consuming to set up a rented camper for actual use.
- You need to clean the camper upon return, and you probably need to have it in around 10 in the morning. That means you need to spend much of the second-to-last day driving near the return location and getting ready for rental return.
- I am not aware of any company that would rent out a camper with a toad.
- The nearest stations for the Canyon are probably Las Vegas and Phoenix. If you want to camp at one of the campgrounds in the park (Maher), be sure you have a reservation (unless you are travelling off-season). Reservations can be made online.
- If you want to rent at one station and return at a different station, you will need to rent with one of the major companies. And even then there are a lot of restrictions.
It is doable, but one week is very short. We travelled three weeks with two rented Class C campers in February/March of 2014, from Las Vegas to Phoenix. That was a very good time of the year to rent (low prices, off season). Pictures from the trip are here:
https://plus.google.com/u/0/photos/104581754261901190566/albums/5991853658484168417