belt drive lathes are quieter than gear head ones, at least in the hobby machines. You get what you pay for!
The only belt drive lathe, new, that I can think of is the Chester Craftsman. That is a 12 x 24, gap bed lathe,but Metric rather than Imperial, if that makes any difference.
They usually came with 3 and 4 jaw chucks, faceplate and steadies, with a 2 hp single phade motor.
Brushless DC machines are quiet
The earlier Myford ML7s, I found restrictive in only having a 2MT spindle. The more recent ones have a 4MT, I think.
The Craftsman will have a 5MT spindle, and should come with a 5-3MT adaptor sleeve.
If you can find a good one, a second hand Warco 600 is very similar, (Came in either Imperial or Metric form) as is an Engineers Tool Room BL12 -24 (Metric, but dual dialled) I specified a VFD for mine when ordered, But no longer available. All those have a gap bed allowing work up to 18″ diameter to be swung. Quite heavy at 300 Kg.
A smaller machine, but seemingly versatile would seem to be a Sieg SC4, available from more than one importer in different “bundles” , prices and different warranties.
Be wary of a shiny “refurbished” secondhand machine. Some might be good, but! The paintwork may look good, but it could be worn or damaged when examined more closely. If you go to see a second hand machine, take someone with you to help check it. If you don’t it is easy to buy a pup!
Have a look at the Classified on here to get some ideas, of prices for used machines.
HTH
Howard