* 1.66 GHz Core Duo/SD, $649, Apple
* 1.83 GHz Core Duo, $699, Apple
Which one would you suggest might work better for my project?
In order to burn a DVD, make sure the Mac includes a "SuperDrive" - otherwise, it can only read DVDs. The 1.83 MHz model includes a SuperDrive, the 1.66 does not.
Full specifications and configurations are here.
A Mac mini should work with your existing VGA monitor, keyboard and mouse. You can just plug them in as needed.