I appreciate the input Skybird.
I knew I was a bit vague on a few points.
I'll edit the first post so that it is a bit clearer.
The new PC will run Linux. There was never any doubt of that.
Option 3 was just that... An option, I think I accidentally removed the line while editing were I had typed "I'm not spending $3k on a PC". Never have, never will.
Option 2 was the "original plan".
As far as the Laptop idea, her "desktop" is the only one we could find when she went looking for one several years ago, that wasn't "a laptop in a desktop case".
It was the only one with an actual internal PSU. All the others used a Laptop power cable.
A laptop, for her, is like asking one of us to play Crysis on a 486. Just too slow for what she does. Plus she still has a Win7 laptop.
My "old" dual core is still working, it's the network backup/extra game machine.
I actually bought a 40" Sanyo TV for the monitor... I don't "junk" my hardware until it's fried.
Barracuda