Analog is the regular traditional port that CRT monitors and some LCD flat screens use to hook up the monitor and pc. With this sort of connection, there is the concept of screen refresh rate which can lessen the image quality.
But with DVI (Digital Video Input), you get a perfectly crystal clear digital image with no screen refresh rate. Meaning the screen doesn't have to continually refresh itself. Only LCD flat panels have DVI connections. So to answer your question directly, DVI is definately the way to go if you can do it. I use a flat panel monitor with DVI connections and it's awesome. In addition to your LCD flat panel monitor with DVI, you'll also need an appropriate DVI cable and a video card with a DVI output port to experience the greatness of DVI. Hope that answers your question.