Well, I'm assuming you use windows, in which case accessing the printer port is a major pain, becuase windows restricts access to it for stability reasons. The serial port on the other hand, is alot easier to play around with becuase everyone has access, so it's what I'd recommend using. Only downside to serial is it's a bit slower, and the LCDs for it cost more. "Computer Modding" lcd's into those bays is actually a very popular thing to do, so there are alot of prebuilt settups, premade open source software, etc. for driving these LCDs. I know you want to make your own, but you can use alot of these guides as a jumping off point.
Here's a thread from a major computer hardware forum addressing the subject, including lots of good links on premade software, LCDs, etc: **broken link removed**