The Mac Mini 2 from 2007 has an Intel Core Duo processor; you should confirm this from the 'About My Mac' choice in the Apple Menu. This can be upgraded to Snow Leopard or Lion. Both are available in the Online Apple Store, Snow Leopard on install disks, Lion as a code to use in the Mac App Store application (but you will have to install Snow Leopard first to get this).
Snow Leopard is a good system but is no longer getting security updates and a number of applications won't work on it. Lion is less satisfactory though more up to date. You should note that if you have any PPC programs such as AppleWorks they won't run on Lion or any system later than that (nor of course on any new computer you buy) other than by emulation such as in Parallels.
If you can run to an up to date Mac, particularly one using a fusion or SSD drive, you will see a startling improvement in speed, but you may have to upgrade some of your applications and as said the PPC ones won't work.