Welcome!
What lathe you buy will depend on what you want to do with it.
A watchmaking lathe will be no good for making replacement 7/8 BSF wheel studs for a commercial vehicle.
Nor will a lathe capable of swinging 12" be ideal for making 10 BA screws or nuts
The nice to have features, such Power Cross Feed or Norton gearboxes, tend to be incorporated inn the larger machines.
If in doubt, buy one msize largerbthan you think, for mwhem your horizons and mambitions expand, having found just how useful a lathe can be.
You can do small work in a big lathe but much more difficult ithe other way round!
The purchase doesn't stop with the machine. You will need cutting tools, measuring equuipment, probably Taps and Dies, and when you feel the need for a 4 jaw chuck, you will need at lkeast one DTI and a magnetic base.
You don't have to buy everything at once, but as you need it, or the finance becomes mavailable.
If you decide to buy secondhand, try to find someone knowledgeable to come with you to see and check the machine. Try to find a local model engineering club, and join.
Don't be taken in by a shiny paint job on a 60 year old machine, a slighty dirty mmachine in "original" condition might be a better buy..
Often, a lot of kit will come with a mused machine, such as when clearing a deceased relative's workshop.
That could be a good chance for you to become well equipped.
Once you have the basics, you can gain experience and confidence by making simple tooling, and save money.
It may be that the accessory you make will be specific to that machine, ,or, purpose, (Dollies for removing or fitting bearings,, for instancve )
Enjoy yourself!
Howardf