Agree with all the above.
On a limited budget, your machine will be a hobby lathe, not a tool room precision machine, so don't expect too much of it in capability or absolute precision. For a start, a 3 jaw chuck will not hold work absolutely concentric..
If you have any queries, ASK. You may get different opinions, on here, so that you have to make the choice (like the lathe ) that best suits your needs and aspirations.
When you can, join a Model Engineering Society, local to you.
Gather information BEFORE selecting and buying the machine. Many Far Eastern lathes are very similar, (some come from the same factory ) but differ in paint scheme, as if that matters, and in the package offered by the importer, and the after sales support provided..
Hopefully members will be prepared to provide face to face, and hands on advice and demonstrations.
Before over extending the budget, try to distinguish between the "Absolutely necessary" and the "Useful at some future time"
You will need a bench grinder and a few measuring instruments almost from the start. Ditto for a Tailstock Drill Chuck
A bench grinder will allow you to learn how to grind High Speed Steel tools. If you need, Carbide tips can come later, once you have grasped the basics. When you eventually progress to form tools, you will be grinding these from HSS..
With a 4 Jaw chuck will come the need for kit to centre work, so a DTI (Ideally plunger and finger types – but one sort will get you started ) and magnetic base of some sort.
To save mioney, and gain useful experience, some tools, you can make. They will help in the work and extend the usefulness of your machine.
Climbing onto a hobby horse,a Centre Height Gauge should be and early one.
Eventually there will, be a need for thread gauges, to identify unknown threads that come into your life.
The you will discover Taps and Dies of the various sorts. (At least 6 different, but similar, varieties if you so wish, or find the need )
Things like collet chucks can wait as can DROs, IF you find that they are really essential.
For Reading,
Zeus charts – contains all manner of useful information. An almost essential first buy.
When the Budget allows for it (Birthdays or Santa? ) books such as:
The Amateurs Lathe – L H Sparey. Old but useful on basic principles.
The Amateur's Workshop – Ian Bradley Ditto
The Model Engineers Handbook – Tubal Cain. A very useful reference book.
Others may recommend Harold Hall's Books, or Dave Fenner's book on The Mini Lathe, or Neil Wyatt's books on The Mini Lathe and Basic Lathework.
Every one of the above will contain information that will be useful to you, on basic principles and as a reference.
You can start worrying about setting up gears for screwcutting at some later date.
Learn to walk first, marathon running comes much later.
Work within your limits, so that you don't take on a task which you then find to be beyond you, leading to disillusionment.
Hope that all these ramblings will be of some help
Howard