Hi,
I'm sorry if I missed it, but how many people will be taking this trip? Make sure there are seatbelts in the quantity and locations you'll want them, or be ready to add them yourself.
I personally think your goal is a bit aggressive, but it all depends upon what you want to see. Perhaps if you definitely added the extra 3 weeks, it would take some of the stress out of the trip. You really should also plan for days of "down time" where you just hang out at a campground and regroup, swim, do some laundry, routine maintenance on the rig, etc. When we visit an area/attraction, we tend to stay in the area and see as much of it as we can before moving on. Others are content to just do a drive-by. IF amusement parks are on your list, admission & parking fees can be quite steep and you'll probably want to spend at least a day.
Will you be towing a car, or just using the motorhome? If towing, make sure the rig and the vehicle are up to the task.
You said some of the sights will be "look out the window" type of stuff. No problem, but remember the view out the windows of most Class C's from the passenger area are quite limited.
If I were you, I'd up the price range of your search to the $20k-$30k range and find a vehicle in the 10 year old range with moderate mileage. The initial cost will be higher, but if you decide to sell it after the trip, I think you'll be better off, and I think you'll improve your chances of not having any unscheduled repair issues. Check generator hours, too. Too few hours on the generator are generally bad. You want a rig with a generator so you can run the overhead AC while travelling down the road, assuming you'll be travelling in the summer.
If you get near the 30' size with slides, you should check into weight limits very carefully. Ditto if you see a 26' on an E-350 chassis.
And since I'm always one good at spending other people's money, I might suggest you also include some Class A rigs in your searches. Generally speaking, they will have larger holding tanks, more storage and possibly better weight carrying capacity. But even there, buyer beware. With our family of 6, I estimated we'd need about 2,500-3,000 lbs. of capacity for people, food, water & stuff...and that estimate seems to have been pretty realistic.
Good Luck,
~Rick