I have been on 17 RS tours, mostly solo and I always get my own room. It is a pleasure to have the space and time to yourself in the room. So I would not hesitate to spend the money to get a room, which adds to the pleasure of the trip. As for what kind of room do you get, it just varies from hotel to hotel. It is a gamble for everyone on the tour. The hotels are not chain hotels so the rooms are not cookie cutter rooms. I have had small rooms, I have had large beautiful rooms. My room in Istanbul was large and wonderful, my room in Switzerland was plain with a single bed, which was perfectly fine and comfortable, but I had a balcony which was wonderful in my room. I had a small room in Venice. So there is no way to know what kind of room you are going to get, it just depends on what the hotel has to offer. My room in Vienna has two twin beds. You just need to prepare yourself that whatever room you have it will be a fine and you have it all to yourself.
As for the structure of the tour, it is up to you to see if you would enjoy it. You have options, a 7 day week long tour or a bus tour. Do you want to go 14 days or longer or take a shorter bus tour to see if you like the tours?
It basically is, meet the guide and tour mates at the hotel the first day around 3PM to 5PM. Have your introductions, then take a walking tour before dinner, which leads you to dinner altogether. The next morning, is another walking tour, then going to some sites. Break for lunch, sometimes meet up again, sometimes have the afternoon free, meet up for dinner or dinner is on your own.
The morning you leave the town your in, breakfast, then get your bags to bring to the bus, Bus ride, bathroom stops and stop at a site along the way. Then pull into town in late afternoon, have that walking tour and go to dinner. The second day in a city you have dinner on your own, the first nite in a new town, most of the time, you have dinner with the group.
Read the tour descriptions, they really tell you what the day is and when you will have dinner with the tour or group. Sometimes, there is a lunch included but that is not usually in the tour descriptions, so that is always a nice surprise.
You get a mix of tour and independent travel. For someone with much more independent travel minded as you, I would choose a tour that interests you that you don't feel as comfortable traveling alone and would appreciate a tour to get you there.
I took the week long Istanbul tour, and I loved it as this is not a city I would go to by myself or even with a friend. Not that it is unsafe, far from it, but more different than cities in Europe. Maybe Turkey, where you may not go on your own but a tour gets you there and you would like it more because it is a place you want to see but would not go to on your own. Just an example, using Turkey.
Hope this helps. As for river cruises, I am sure they are lovely, but that is something I would rather do with someone.