You can use a mini display to vga port like any of these
http://www.amazon.com/s/ref=nb_sb_n...ps&field-keywords=mini+display+to+vga&x=0&y=0
But you mention you have a relatively new screen, I'm pretty sure it will have either a DVI port (white port about the same size as VGA) or a HDMI port (about the same size as a USB port).
Either way, I would recommend the stock mac mini and then upgrade the RAM to 8 GB for ~$100.