I just finished an internship at a museum, so I’ll share what I got from that and from reading articles in the museum magazines they had there. The first thing you’ve got to do is to find yourself some internships. This is difficult, true, but the number one requirement I’ve come across is experience—often, a lot of it. Do it now, while you’re still in school, because it’s very hard to find internships that will actually pay (a lot of people want them, and museums are, on the whole, very reluctant to fork out), so it’s nice not to have to support yourself with something else while doing so. The irony of the museum world (which I have seen complained about a lot) is that they want to hire experienced people but will rarely provide the training people need to get that experience; any museum work you can land is a step in the right direction.
As for degree, it’s actually not to your advantage to just get art… Apparently, a large portion of potential applicants have a degree in the humanities, so that won’t help you stand out. Go for the combo, or specialize, depending on the level of study at which you’re at (though this last will, of course, be more helpful if you’re applying for a very specific curatorial area in a larger museum—the National Gallery, in London, for instance, has a curator of Dutch painting 1600–1800, and that’s what she’s got her degree in, but a small museum will possibly only have one curator for the entire thing). I think the combo, representing a wider range of knowledge, will make you a more attractive candidate.
If you’re looking at the natural history side of things, then I suspect the science degree would be more important than anything else, but I won’t say more as this is entirely a guess.
Addressing the possibility of doing a degree in Museum Studies, then, as an alternative, it depends. Look for one which emphasizes the practicum element; Museum Studies also being an academic field, getting a lot of theory will be helpful but only to a point—you want the experience. Look for programs which are good at getting their students placement, and whose graduates have a tendency to get hired pretty quickly. My boss at the museum had undergone one of these, and it really did launch her career, so she highly recommended it. On the other hand, having specialized knoweldge can in some instances be more attractive to the institution—they want someone who really knows their stuff, and while Museum Studies will help you set up a great exhibit (always important), a museum likes to see you understand the objects you’ll be curating for. This can be helped by your undergraduate degree, of course, and it’s not worth ruling out Museum Studies as an option. Go for what calls to you!
As a (really bad) case example, I hope to become a museum curator. I’m planning on specializing to Medieval Studies as soon as I get out of college (having done my undergraduate work in history, with a medieval and Renaissance studies concentration). The concentration alone would probably be enough to qualify me in that area, and given the limited number of medieval museums it’s probably a little silly to keep specializing, but it’s what I really like to do, and if I can get really qualified in it, then I will probably be an attractive hire somewhere. Note that there’s no art degree in this; I’ve had a few courses, but I’m hoping that this more general degree will work for me. Afterwards, I might go on to Museum Studies as a second MA, if I haven’t already gotten hired somewhere; remember, you can always go back to school. Finally, I’m looking at getting a second internship next summer in a museum-related workplace, and am taking all the undergraduate museum studies courses I can. End result? I’m going with what I’m most interested in and really focusing on getting museum experience to supplement that. If I had to say anything, it would be to worry less about the degree and more on the internships.
Good luck!