If you just want to work in an art museum, in an administrative or support role, a museum studies degree might be useful. But if you want to be a curator, your time and money is better spent on a Ph.D. in art or classics or whatever is your special area of interest. For curatorial positions, academic work counts most, and experience (internships, fellowships, volunteer work, etc.) is also very helpful, but museum studies credentials don't make much difference one way or the other. And the advantage of the Ph.D. is that you can go either academic or museum world--in fact, most people end up in one or the other largely on the basis where jobs are available. But they are hard to get whichever way you go. Choose a grad school where there is a museum (or two) with collections in the area where you want to specialize, and then introduce yourself to the curators, and grab any paid or unpaid internships on offer. The advice to do volunteer work before starting school again is also very well supported--especially since you are changing fields, it will show commitment to your new interests.