Making a Mac Mini mid-2007 able to display 2560x1440 in 2D work
With a Mac Mini that old, you are out of luck if you want anything better than the built-in HDMI.  However, there are USB-to-DVI converters, also known as external graphics cards, that will work fine to connect a second display.  I have had good results with this one.  Two 1920x1080 monitors are a lot better than one!

Newer Minis (the 2008 Core 2 Duo model with GeForce graphics, and later) have two video ports, one of which is a DisplayPort connector which with the right adapters can run a 30" monitor at 2560x1600.