Qualifications
Since this field is all about research and organization, you're going to need a brain that works, can stay focused, and doesn't look at a complex series of letters and dates and immediately think, "Cats!"
To begin with, you're definitely going to need a bachelor's degree, and probably a master's degree as well. The bachelor's degree can be in whatever field tickles your fancy, while your master's should probably be in history or library science.
Personality-wise, qualifications are more about people-pleasing than you might think. You've got to be logical, so that you can develop a system of organization that people will be able to use long after you've become history. You've got to be social (or at least sociable) so that you can help people find what they're looking for. You've got to have a great attention to detail, so that you can pick up on the little things that most people might miss (and then tell them about it).
And you absolutely need to be able to work within the guidelines laid out by archivists past, otherwise what's the point of saving any of this junk?