My wife and I took off for a year in '99/'00 and did about 30,000 miles in our minivan. We spent about $26,000 for the whole year, including a couple of months busing around Mexico. I don't know how cheap you want to go, but we mostly tent camped in the US and Canada, with some breaks staying with friends and relatives.
Our van gets around 21 mixed driving and we got as much as 29 mpg on the road trip. We would have had to cut our trip in half if we had to fill up an RV everyday. But you have to like sleeping on the ground. :-)
A conversion van may be an option, but I guess it depends on how big your family is too.