Tony, stainless is not a hard material; it is easier to turn than some of the common things we turn. The problem with SS is that it work hardens and this occurs when cutting temperature rise at the point of cut. When this occurs it becomes difficult to take small depths of cut (like finish cuts) until you cut under that hardened surface, at which point the tool will cut well again. 304 SS will work harden much faster than 303 SS so the material you choose will affect your results, too.
It isn't so much the size of the lathe that determines how well it will cut SS. Rather, it is the rigidity of the set up and the cutting tool geometry you are using that is as, if not more important than, the lathe itself. This applies to turning, boring and parting. Heck, even a small lathe like a Taig or Sherline can handle these operations with no problem at all. Others have suggested carbide tooling but SS responds better to a sharp HSS tool with the right tip geometry on smaller lathes in non-production settings. At the speeds available on hobby lathes, HSS will also finish better. For that matter, cobalt tooling will cut SS just as well and last longer before dulling.
In the size class of lathe you are looking at you will find that sharp HSS/cobalt tooling will work better in almost all cases. The problem with these tools is that you have to learn to grind them, and not everyone is willing or able to do that.
