I have bought and sold two lathes, and now bought a third. I found that a Chinese manufactured lathe (same maker as my mill) has a product called a CQ6125 that seems to appear in a dozen different places, called something similar (Brand name of a retailer plus the CQ6125), but often with different accessories, tools, etc.
Here is the spec sheet for my unit ($1300):
Lathe
22"x10" (550 x 250MM) QUICK CHANGE GEARBOX METAL LATHE W/STAND
Industrial quality machine, perfect for general machining in tool rooms and workshop, maintenance and production shops, cast iron quick-change gear box makes threading easy, machine ground, hardened iron cast bedways and come with 4 ways tool post, it has long travel automatic power feed, includes stand cabinet

specification: 

-distance between center: 550mm (22") 

-swing over bed: 250mm (10") 

-swing over cross slide: 156mm (6") 

-spindle bore: 26mm (1")

-taper of tailstock: MT3

-tailstock spindle travel: 65mm (2-1/2")

-number of longitudinal feeds: 9 (0.063-0.350mm/rev, 0.0025"-0.013"/rev)

-thread cutting: 38 kinds (metric 0.25-3.5mm & imperial 8-72tpi)

-range of spindle speed: 6 (125rpm-2000rpm) 

-motor: 750w (1HP)/240v/1ph (single phrase)

-max. tool size to use size:10mm x 10mm (3/8"x3/8")

-max. compound size travel: 95mm (3-3/4")

-max. cross size travel: 145mm (5-1/2")

-steady rest capacity: 6.35-50mm (1/4"-2")

-follow rest capacity: 6.35-50mm (1/4"-2")

-length of bed: 1050mm (41-1/4")

-width of bed: 155mm (6")

-height of bed: 200mm (8")

*accessories includes:
stand cabinet,
splash guard,
chip tray,
5" 3-jaws lathe chuck,
6" 4-jaws lathe chuck,
8" face plate,
dead center,
fixed steady,
travel steady,
change gears,
toolbox etc.

*Shipping weight (all up): 298kgs
Now, I've unpacked this new toy, assembled the cabinet/stand unit, bolted the lathe to the stand, and started to prepare it for use.
I've checked the level of the machine with several highly accurate levels placed across and along the ways, and had to shim up the back of the lathe (concrete floor). That seems to be OK now.
But I would never run my mill without bolting it down: this lathe cabinet/stand doesn't have facilities to bolt it to the floor. Is that what you would expect?
I've run the tailstock up to the head stock, centres in each, and the two points meet by eye (and, on the way back the point of the centre in the tailstock seems to be at the tool height (right knife in tool holder).
But, is this last process too imprecise (Yes, but how do you do this check properly?).
What other steps does one do to get the best set up of a new small lathe?
Also, I can comfortably hold 13mm x 13mm (1/2") tools in the tool holder: if I am managing the speed, depth of cut and rate of cut, using cutting oil when necessary, am I really silly to ignore this limit of 10mm tools?