I was in your position several years ago when I decided to pursue a
graduate degree in history.  After enrolling in the program I found the
attitude of the grad. instructors was that they were training future
history teachers (college level only) and that if you didn't want to
teach history then you had no business in grad school.  This upset me
quite a bit, I had no intention of teaching, I was only taking the course
for a love of the subject.  That reason for enduring grad school seemed
unknown to them.
   I did persevere however, and on my own began volunteering at a brand
new art museum in town.  Five years later I am the registrar at the
museum and loving every minute of it.  If you want to pursue museum work,
why not take grad classes at William and Mary, which has one of the best
museum studies classes around?  Another alternative would be to go ahead
with history grad work, art history as a minor, and see where else you
can volunteer (most museums will welcome you with open arms if you are
willing to do anything they want).  Grad school is a good idea just
because the higher degree you have the more marketable you will be.
   The lesson I learned is that you can do whatever you want if you will
ignore those who tell you "it can't be done"!
   For networking purposes you should really join your regional museum
conference, you get a quarterly newsletter which will put you in touch
with people just dying to give you advice (like me).  Contact
Southeastern Museums Conference (SEMC), P.O. Box 3494, Baton Rouge, LA
70821-3494. (504) 383-5042.  I think the fee is $25.  If you are
interested in registration-type museum work, you can also join SERA
(Southeastern Registrar's Assoc, a division of SEMC) by contacting
Michelle Baker, at South Carolina State Museum, PO Box 100107, Columbia,
SC  29202-3107, that fee is only $10.00 and well worth it.
    Good luck.