Welcome to the Forum.
You will always find help and advice on here.
"What lathe" $64,000 question!.
Nice to buy new, but many a good tune played on an old fiddle, especially when you know how, if the budget bis limited!
I've seen superb work made on a 100 year old lathe.
Find a local Model Engineering Society and join.
You will find face to face advice, maybe even demonstration, or a chance to try your hand..
Where are you located? There may be someone nearby who can help personally.
Buy at least two books, and study them, before you buy. They will help to crystalise your thoughts.
A set of Zeus Charts, you will use them for then rest of your life, from time to time.
These books will tell you how to set up your lathe so that it
L H Sparey "The Amateur's Lathe" was the "bible"
Ian Bradley "The Amateur's Workshop" Covers hand tools as well the lathe.
Stan Bray "Basic Lathework"
Harold Hall "Lathework"
If you choose a mini lathe
David Clark, Dave Fenner and Neil Wyatt have all written books on the mini lathe.
Knowing a little more about lathes, their operation and features will help your choice of machine.
You won't use all the "bells and Whistles" all the time, so may not need them, but when you need one and it is not available, it is frustrating. Sometimes, you can find a means of working around..
Have a look at the Workshop Practice Series of books. You won't need many of them, but you may find what you need to get started among the many titles.
Tubal Cain – Model Engineer's handbook is a good reference book to have, also.
The jobs that you do or want to do will have a huge effect on what you seek, and the features that you want.
Your budget needs to allow for measuring equipment, and accessories, for which you will find a need before too long. (Bench Grinder, Four Jaw Chuck etc )
Using High Speed Steel tools will allow you to learn how to grind tools. (Some older lathes are not suitable for carbide tooling, they are not rigid or fast enough for it, and the bearings will not like protracted time at high speed )
Some you can make, as part of the learning and familiarisation process
Riding some of my hobby horses, Centre Height Gauge, Tap Wrench (es ), Die Holders (Hand and Sliding Tailstock types (Eventually, you may want to make a Sliding Tailstock Tap Holder )
They will all come in useful, and you will use them from time to time for the rest of your life. .
How big? When you have decided, try to find something next size up! You will eventually find a need, and yearn for it! Fantastic work work has been dome on lathes that, supposedly, are too small.
Do you envisage cutting a lot of threads, other than with taps and Dies? Try to decide between changewheels or a Norton Gearbox.
There are books on screwcutting which will help setting up.
HTH
Howard