Mac OS reinstall tool says volume protected

The hard drive with the Mac OS Base system is the installer. You can't install there.

If there is no volume on the Hard Disk, then you might need to create one.

You should see a Hard Drive at the top of the list that is named based on manufacturer and size.

Below that should be Macintosh HD, indented from the Hard drive. The name may be different.

Does any of that sound familiar?

You might need to use Internet Recovery, if the mini is capable: http://support.apple.com/kb/ht4718

I didn't realize that model number wouldn't help much.

This article talks about Internet Recovery: http://support.apple.com/kb/ht4718

If it starts up with a spinning globe, then you are in Internet recovery. Use the Disk Utility there to partition the hard drive into 1 partition, Mac OS Extended (Journaled), and set the Name to whatever you'd like. The default is Macintosh HD.

Under Options, set it for GUID partition table.

Once that is done, quit Disk Utility and then install the OS. It will install the OS that it shipped with (either Lion or Mountain Lion). If it is Lion, you can then purchase Mountain Lion from the App Store and install that. Or, wait until Mavericks is released (sometime in the Fall), and upgrade directly to that.

What is the model number of the Mini?

It sounds like the previous owner wiped the free space and somehow merged it into the Recovery HD.

I'm thinking you'll need to use Internet Recovery to boot and partition the disk, then install.

Internet Recovery will install the OS that shipped on that Mini.