If you are looking for a lathe with a Norton gearbox, and power cross feed, you could seek a secondhand Warco BH600, Chester Craftsman, or a rarer bird like mine, an Engineers Tool Room BL12 -24.
Basically, they are all clones, in different paint schemes.
The BH600 (and its longer sister the BH900 ) were available in Imperial or Metric form, the Craftsman was only Metric, I think.
The BL12-24 is basically Metric, but dual dialled.
As a secondhand machine, it may well come within your budget., if you have the space available.
Mine came, new, with 3 and 4 jaw chucks, Faceplate, fixed and travelling steadies, and a 5- 3 MT sleeve for the Headstock. The standard toolpost is a four way.
The gap beds are induction hardened, and the power feeds are provided by a feed shaft, with the Leadscrew as a separate means of traverse.
The belt drive provides 12 speeds, including back gear. It is a heavy beast, 300 Kg, but the better for being rigid.
(As part of the deal, mine was fitted with VFD, so that there are only 6 speed ranges but all subject to the VFD, So a multiplicity in reality. )
Using the 120/127 main Idler it is possible to cut a wide range of Metric and Imperial threads.
Although quite accurate, it is not a toolroom lathe, nor one for watchmakers, since it will swing 12" or 18" in the removal gap.
Having a Tee slotted cross slide it is possible to fit a back tool post (Although through being careless I have made problems for myself. A little haste and a LOT less speed, putting it out of action for a few days while I made repairs! )
Problems?
Noisy tumbler reverse gears (replaced by nylon ones, at some cost. )
The drive shaft / pinion for the Saddle traverse is soft, and does not survive collisions particularly well!
Another possible secondhand machine might be a Raglan, Little John, or 5 Inch, if you can find one in good condition. Based on my limited experience, a very useful machine. Ask N D I Y about his!
HTH
Howard