Auctions are a bit of a mine field and a gold field - you sometimes step on a mine and sometimes find gold.
The best deal I ever heard of was getting a lathe at one of these estate sales - I think someone on the site paid 50 CAD for a bench-top lathe - exactly what you would need, a bit bigger then a mini. I think it was an Atlas lathe that was used for some wood working. Most pp would buy it in a heartbeat for $500. I think it was model 618 (about 7 inch swing with 18 between centers). For $50 CAD.
Action sites are such as Richie Bros, Michner Allan, GD Actions, Century Auctions. plus estate sales.
You can also try machinery dealers - see this video -
There are alas no dealers like this around us (OK there are sellers of used equipment but price is rather... high) watch most of the video - you see they sell small lathes like you would like as well - from high end desktop Hardinge to lowly Craftsman with timeless Southbend in between.
With some used machines you may be forced to do some work on them. The better the condition the higher the price - usually.
