Welcome! You are planning to take up an interesting widely varying, and sometimes frustrating hobby. But an extremely satisfying one.
As you read the MANY threads on the Forum you will see the huge range of activities undertaken, and learn a lot.
You will get plenty of advise on here; Sometimes contradictory!
Old vs new, Chinese vs old European, levelling a lathe, tooling, etc. You name it, and we will come out on riding our hobby horses! .
Where are you located?
Try to find a local Model Engineering Club and join. You will find fellow enthusiasts, willing to help, guide or demonstrate methods.
If you are new to machining, some books will help increase your knowledge and understanding.
"The Amateur's Lathe" by L H Sparey. Old but the basic principles are the same.
"The Amateur's Workshop" by Ian Bradley. Covers fitting work and tools as well as lathe work..
"The Model Engineer's Handbook" by Tubal Cain. An invaluable reference book.
Certainly buy a set of Zeus charts, for the data on drill sizes and equivalents, threads etc and mathematical tables. I still use mine regularly, bought in 1958.
You will need Allen keys (possibly two sets, Imperial as well as Metric. Feeler gauges, ditto )
Mine would be , since you seem to have decided what you want to make, find a lathe that will do that sort of work; and then buy one a little bigger. i.e. if you think that a mini lathe such as SC3 suits, buy a SC4.
Your horizons will expand and you will avoid the frustration of almost being able to do the job. The larger machine is likely to be more versatile, also.
Having said that, superb work is made on old machines, sometimes beyond the claimed capabilities of the machine. There are folk on here doing excellent work on machines that are a century old!
But the budget needs to be considered, not just for the lathe, but for the measuring equipment that you will need to complement it. A digital calliper, DTIs (ideally plunger and finger clocks) as well a magnetic base to hold them (Scribing blocks are OK but cannot always be fixed in the same places as a mag base. )
If the lathe does not include tooling, you will need to buy (My advice would be High Speed Steel so that you learn how to grind tools correctly. That lets you in for a bench grinder as another purchase )
You will need a drill chuck for the tailstock, if the lathe does not come with one Depends on the sort of work that you want to do, but steadies are perhaps less necessary, certainly early on.
If you do not already have them, you will need drills, possibly Imperial and metric. You will eventually acquire more sets, because of the need for drills which increase in size in smaller increments.
As you gain experience and confidence, you will be able to make tools and accessories. This will save money, increase experience and probably produce a device which cannot be bought, but is essential for your needs.
The you will start collecting Taps and Dies. You need to choose which you need at first. (Whitworth, BSF, BA Unified, or Metric ) You won't need all sorts at once.
Complete sets in a box are a nice way, of storing and keeping safe. But some you may never use, I have never yet found a need for a M11 thread! On the other hand, jumbled together in a tobacco tin is no way to keep them sharp and undamaged.
Enough of my ramblings.
HTH
Howard