The Unimat! I have fond childhood memories of that lathe. Not OWNING one, mind you, but of longing to own one. It's probably just as well, as I would have quickly outgrown it!

As you know, they also made a ton of accessories for the Unimat, even a milling head, as I recall.
That one looks to be in very nice shape. I agree, I wouldn't repaint (unless I could find the exact hammertone color.)
Looks like a fun project!
Paula