DVI, HDMI, and Displayport are digital. VGA (Dsub) is analog. The digital standards will yield better picture quality, though the exact amount of improvement depends on your cable and monitor.
Going from digital to analog is easy. Going from analog to digital (VGA output to DVI input) is harder, and will be more expensive. If your computer/video card doesn't have digital output, just stick with the monitor's VGA input. The monitor's internal electronics will convert the analog signal to the digital display - the same thing a VGA to DVI adapter would do.
The only way a VGA to DVI adapter would improve your picture is if your VGA cable were causing picture degredation (often happens with very long cables). In that case an adapter would help, but it would need to be located before the cable. i.e. the adapter needs to plug into the computer's VGA port, and you use a DVI cable to connect it to the monitor.