A secondhand Warco BH600, Chester Craftsman, or Engineers ToolRoom BL12-24 (clones other than paint scheme) will swing up to 18 inches in the gap, as will their successors, and ex Tech College, or Industry lathes.
The problems with ex Industry machines are that they will have worked hard for their living, and are likely to be 3 Phase, and so will need a change of motor to work in a domestic environment off a 13 Amp socket.
Ex Tech College machines will have done little work, but probably been abused, by things like running the toolpost into the chuck and so on.
Once you have a lathe, (and hopefully, a Milling machine) the world will almost be your oyster, with a huge range of jobs now possible.
ENJOY!
Howard