Thanks for the additional information.
I would suggest looking primarily at class C and class A motorhomes, since you aren't interested in a towable of some sort. Class B's are more expensive and are small.
It's not perfectly clear to me from your writing, but if you're hoping that a $20K RV you buy now will be good for extensive use several years from now, I think that may be a bit of a long shot. It's possible, but not necessarily probable. On the other hand, if you're thinking more of this being one to get your feet wet, so to speak, and have a better idea of what you'll look for in the next RV, then you have a pretty good plan.
When looking at used motorhomes, condition is the most important thing to look for: how well the maintenance has been kept up with, and whether it's free of leaks, and the systems work properly. A lower tier brand, well maintained, is a much better buy than a top-shelf unit that has not been cared for. That said, I would think a larger unit might be more practical than a tiny one, particularly if you have some provision at your daughter's property for sewage disposal. If this is a house on city sewer, there's quite likely a cleanout somewhere on the property (outside) that can serve, though it may not be in a convenient location. If it's a private septic system, quite often the cleanout would be in the basement of the house and hence not usable for an RV.
Plan to spend a little money to have either a 30A or a 50A RV outlet installed at the house, unless by some miracle it already has one. It will be money very well spent compared to trying to use a single extension cord to the garage or whatever all the time. A 50A outlet probably makes more sense to install newly as the labor is pretty much the same for both, and you can readily use a 50A outlet with a 30A RV via an inexpensive adapter (or you can get boxes with both 50A and 30A outlets). With a 30A outlet, do make sure that whoever does the installation knows this is a 120V outlet for an RV and not, I repeat, not a 240V circuit.