There really isn't any minimum processor. As long as it's something more recent than a first generation pentium, you shouldn't have any problems other than speed. Ubuntu is pretty heavy and designed for features instead of efficiency, but honestly, I really wouldn't recommend using anything else until you get a feel for Linux. Trying to use unfriendly distributions can be really painful if you don't know how they work.I mean just getting something to print can be a full day task if you don't know how to do it.