DVI and HDMI are digital signals, you'll get a slightly better picture if your monitor has a DVI or HDMI input. You can buy an inexpensive DVI to HDMI adapter if you need to (Around $5 U.S. or less).
VGA is an analog format, those are the blue inputs you see on older monitors, giant tube type crt monitors, etc. Those will work too, and you can get a DVI to VGA adapter if needed, also inexpensively, but if you have the option, and if you're looking for a new monitor, try to get one with either DVI or HDMI input.
If you ever decide to hook your mini up to an HDTV, normally you have two options based on the inputs on HDTV's, either a VGA input, or an HDMI input. Again, choose the HDMI input, so you would in that case need a DVI to HDMI adapter (and to get sound you would need a 3.5 mm audio cable to run from the Mini to your HDTV - and depending on your TV's audio inputs, the cable should either be 3.5 mm on that end or older RCA style red and white inputs). If any of that is confusing, just ask and anyone will be happy to help, including myself.