What size separates lathe from mini lathe?
You will find that a more useful way to look at lathes is to compare feature sets rather than just size. Most mini-lathes and hobby class lathes are 10" and under; almost all of these are imports. They typically have spindle mounts that involve 3-4 bolts to hold the chuck on or are threaded. They generally will have power feed but that is driven either by the leadscrew or a key that runs in a slot on the leadscrew instead of a separate drive shaft. Many of the cheaper lathes will be change gear lathe instead of having a quick change gear box but if they have a gear box, threading options are limited. Most of these lathes will not have hardened and ground gears, spindles and ways. Of course, the cost for these cheaper lathes is much lower than a full featured lathe. There are many, many other differences that I won't go into here.
There seems to be a clear distinction between the entry level hobby class lathes and what I consider the more serious hobby class lathes; this seems to be somewhere around 11" or so. Here we begin to see hardened and ground spindles with precision spindle bearings, camlock spindles with realistically useful spindle bore sizes, hardened and ground ways, separate power feed shafts, wider/more rigid bed widths, heavier castings, more useful quick change gear boxes, etc. To see this distinction, take a look at the feature set between the PM 1030 and the PM1127 and you'll see what I mean.
The PM 1127 is a lot of lathe for the buck. It isn't as good as the more fully featured lathes but it is a very good example of what I think is a good entry level hobby lathe. Note that there is a thing I call "feature creep". For a few hundred dollars more you can have a PM 1236 and for a bit more you can have the 1236T. This gets you into the discussion between Chinese lathes and Taiwanese lathes, the latter being of higher quality and clearly more expensive.
Of course, there are other brands of lathes that are heads and shoulders above import lathes. The Hardinge and Monarch lathes, Colchesters, etc. You can still buy a Hardinge tool room lathe for only $60K.
So, what you have to do is learn about lathes and which features are important. It ain't just about size but the features you get or don't get. Some things, like a camlock spindle, are important enough to me to be a deal breaker if the lathe doesn't have one. Does it come with a full change gear set? What are the spindle bearings specs? What kind of warranty? Where is it made?
You may or may not want to look at "old iron". If a project suits you then there are many used lathes on the market as well.
Lots to research but once you narrow it down to what you think you want, ask the guys on the forum who own those lathes and get real user opinions. Then you can decide.