I've been to Europe (Portugal, Spain, France, Italy, Germany, Netherlands, Austria, Czech Republic, Slovakia, Hungary, Bulgaria, Croatia, Serbia, Romania, Greece, Turkey, and the Baltic states) several times in the past 13 years, not RVing, but observing the RV lifestyle. What you want to do is feasible, but maybe not on the timescale you are considering.
I would rent. There is a whole lot more paperwork (visitor status issues) in buying, licensing and selling and customs issues (depending on where you are going) associated with ownership. I would most likely rent a campervan (still being made on vans in the VW Transporter size class), but if my wife still lived, it would be a under 7-meter "profile" which is a miniature version of what we call a B-plus. Even the 7-meter Euro-style RV is not going to get into most of the old cities and hill towns, you'll be hiring cabs, using public transportation where available, riding bicycles and hiking if you still can.
The amount of time you want to spend can be an issue. The length of visit depends on where you are going. If you enter, visa exempt, one of the countries that are part of the Schengen agreement, as a U.S. citizen you can stay in, and move freely among, the Schengen countries for 90 days. This is not the same thing as the E.U., because there are Schengen members outside the E.U., and E.E. countries not in Schengen. With some manipulation of you movements, and visas outside of Schengen, it is possible to extend your stay, but generally at 6-8 months you are pushing beyond the visa-free travel granted in Europe to U.S. citizens. People working around this usually arrange visas outside Schengen, popping in and out for longer stays in Europe, but the limit for Schengen (most of western and central Europe) is still 90 days.
You have a good idea (except for the extended length of time) but you need to do a lot of research on the details before you have a plan. Brother-in-law put six months of detailed planning into a three week European motor trip. Don't think you can just get there and wander, planning no more than a day or two in advance.
