As I live on the Rhine I would go for the Rhone or the Danube. The Volga is also very popular. It all becomes much more interesting if you read up a bit about the places beforehand. My sister-in-law did the Danube one recently and was most enthusiastic. She found a website which sold on a "lucky dip" basis. She paid very little, without any guarantee of a good cabin, but was lucky enough to get a really good one on an upper deck with balcony and a good view. The company on the ship was also very nice.
A river cruise, as has been said, has the advantage of unpacking only the once, but seeing lots of places. And it's easier to follow on the map where you are; you can look out for landmarks!
Henetha - you probably can go on your own, but you may have to pay a double-for-single surcharge (i.e. you stay in a double cabin, but only use it as a single at a small extra charge.)
The thought of an ocean cruise gives me claustrophobia. Worse, actually, I imagine it to be like being in prison.