As retired full timers in a diesel pusher, our situation certainly is not related to yours. However we camped while raising 4 kids so I have ideas on the subject.
1. New or used? I recommend used so someone else takes the first big depreciation hit.
2. Sleeping accommodations. 3 is complicated. Ever consider leaving one at a rest area? Just kidding of course. Bunk bed floor plans are great but then one is odd man out unless 2 are compatable enough to sleep in the same bunk. Perhaps even by modifying the platform to make it wider. Of course one could prefer the larger area of the sofa or dinette.
The issue of storage for long periods is common for motorhomes. My personal belief is that the generator should be run at least monthly and it should be run under minimum of 1/2 load for 30-45 minutes. I would not run the chassis engine unless I was able to take it out for a drive long enough to get it up to operating temp for a few miles.
I would add a fuel stableizer and fill the tank before storage.
With your situation, here is a motorhome brand and model I would personally consider:
2010 Winnie VistaMonaco Monarch 2010This year model is not special just an example. They are both available in bunk as well as conventional floor plans. Shopping used makes it more important to be willing to travel widely to make a purchase.
Good luck with your decision and have safe travels.
Steve Ownby
2003 Monaco Signature
Full-time since 2007