Some considerations that may help drive your decision.
- Your 2001 Honda odyssey can be flat towed behind a motorhome. It would require some equipment though (base plates, tow bars, lights etc) These things aren't cheap but the whole thing could be put together if you did the work yourself and bought used parts for $1,000 - $2,000.
- Your Odyssey does not have enough towing capacity (especially with 6 people in it) to tow any sort of camper that would be comfortable enough for a family of 6 - that's my opinion but I think you might agree.
So you are left with a few options if you want to buy an RV. Trade the Honda for a truck large enough to tow a camper for 6, as well as seating for 6 in the truck. That's going to be a big expensive truck and the truck camper combo would likely be more expensive than a motorhome that can tow your current Honda. Or buy a motorhome. A Class C if you found the right one might have capacity with food and gear for 6 as well as 6 people but Class C's have less room and typically less capacity. In your budget you may have the same issue trying to find a Class A but your chances I think are better in terms of capacity. The curb weight on the Honda is 4300 lbs dry. The max most Class C hitches can tolerate is 5000 lbs and that gets added to the equation of your total capacity. Meaning, with 6 people, all your gear, food, water and the Honda, it's going to be hard to find a Class C that checks your boxes and has enough capacity to handle all that. That's why I mentioned a Class A, typically more room and more capacity, but admittedly your budget might make it tough.