Painting, as in the framed canvas, is not going to be very common or valued in most regions. I know Venice got into painting early on because the air was too humid to make fresco practical, but under most circumstances I don't know why anyone in the middle ages would want something so small and unfunctional.
On the flipside a lot of medieval art is going to be in mediums we see almost nothing of today. If the Bayeux tapestry is any indication, then tapestry art obviously had a lot of significance beyond the sort of kitschy stuff we see a lot of today. Further, tapestries keep your room warm and are large, very portable, and tough.
Wood working and jewelry are also going to be comparatively more important. A good, well made, and beautiful bed with loads of ornamentation is going to be an incredibly important part of a household. Something that will probably get used by more than a single couple at the same time, and an important piece of technology that does a lot to combat winter cold and lower infant mortality. It will be the subject of immense conflict in wills, and making an important bed could easily be the focus of skilled professionals month or even a series of months.
In the middle ages, however, you are far more likely to move artists or artists' workshops around than pieces of art. The sort of cults of personality production that we associate with modern art pieces did not exist.
Certainly, I imagine that art was bought and sold, and it was most certainly traded and given. But aside from a few religious pieces the context for pieces matters too much for the piece to be removed from it.
Architectural and decorative arts were extraordinarily well developed and important. Well placed and sponsored shops and communities of artists could be the subject of considerable intrigue among their patrons and were a profoundly good living for a lot of people. Lots of incredible sculpture in that sense, but art is not seperate from its context.
Think of it as more the sort of culture that surrounds theatrical work, the technical side, than the culture that surrounds gallery work. Do you know the names of the people who crafted the sets for your favorite play or movie? Probably not. Do you know that those things made a huge difference? Yes. Do you know that those people are probably insanely bright and talented? Yes. Does that make a difference in terms of who you think of as 'owning' or having 'created' the play? No. It's the director's, studio's, or producer's piece.
Now does that director, studio, and producer know who made that stuff and what is going in the world of people who make that stuff? Yes, dear lord yes!
Similarly, everyone in the middle ages is going to know what their favorite building is and the art in that building is going to be a major percentage of that calculation. But that building and that art is going to belong to the institution, club, patron, or architect that produced it, and they are the people who are ultimately responsible for that work.
For us now, and for most of the people of the period likely, the artists who created the gargoyles for Notre Dame are anonymous. But given the incredible importance that art had to the enourmous investment that was creating a Gothic cathedral I guarantee they were not anonymous to the people who put it together.
I know I think that that sort of public rhetorical art is a far better use of art, education, resources and community feeling, and in many ways I fear that the current tendency towards gallery art and individuals benefits the artist at the expense of art.