Warning:
Graphic design is not easy to break into. There are a lot of people trying to get in and many of them will work for ridiculously low pay.
As Brooke said, your best bet is to learn as much as possible. Both print design and web design are pretty much a must nowadays.
On any given day, I use four programs: Illustrator, GoLive, Photoshop, and InDesign. I prefer InDesign over Quark, but there are many people out there who would disagree with me on that.
I also sporadically use Flash, Streamline, and when I'm up against a wall, Quark and Dreamweaver.
And if you really want to learn, find a way to intern at a printshop for 6 months or so. Schools rarely teach you the *extremely* important aspects of pre-press like trapping, bleeds, etc.
Hope that helps a little.