The choice you have will be between an industrial sized lathe: Colchester, Harrison, Myford etc. Or a lathe aimed at model engineers: Warco, Emco, Chester, Wabeco and Myford again. If you have the space, then a used industrial lathe can be a good buy, but be aware that these will probably have 3 phase electrics. You can’t just plug this into a 3 pin socket, unless you’re lucky enough to have a 3 phase supply. You will have to either change the three phase motor to a single phase one, or invest in a single phase to three phase convertor.
Lathes aimed at model engineers are usually designed to be plug and play with domestic electrical supplies. Attending the larger model engineering shows will allow you to see these machines up close. Whatever route you choose, a lathe supplied with a good range of accessories is preferable. Chucks, faceplates and tooling are expensive to buy individually, so try and negotiate a good package deal