Tools:
Go easy on tools. They cost, and you don't need many.
The basic set is just a handful (4?), but you duplicate them in different sizes, according to the work, and also for bowl vs. spindle work. Then there's any number of bobbin furtlers and other gimmicks. Avoid those.
Start with the Axminster set
=A360 quid for a sensible set of useful tools, in good metal, with good handles, and at a great price.
Then buy another of the big gouges and the scraper...
Your lathe tools should be solid HSS, as they do wear and HSS reduces your sharpening time. You'll need a grinder. One with the 10 inch geared wet wheel is now very cheap. Tormeks are lovely, but what a price! Woodturning grinding is _not_ the precision art that plane or chisel sharpening is.
For spindle turning you need a big gouge with a fingernail grind on it, not a bowl grind. So get the big Axminster bowl gouge and reshape it (angle grinder) before sharpening it to a fingernail shape (it's all in the Raffan book).
Also convert the supplied round scraper to a square scraper (cheaper than a square scraper of equivalent quality). You might even (if you have a chuck and are doing bowls) grind up another as a dovetail scraper.
Then you need some other tools: a toolrack (plywood with holes in) and a good worklight. I like to work with a 150W halogen on a stand (cheap Screwfix) over my shoulder. It's also a good place to hang my toolrack
- the base is fixed rigid and made heavier too. The rack needs 6 or 8 holes, so that every tool for a job is there and in its own hole - saves hunting. Worklights are important - you need to put the light just where you need it, often swapping side to side.
Raffan and Frid will then explain the virtues of a carving cut rather than scraping, and the arcane art of "rubbing the bevel".
Sanding needs a bunch of decent paper. Cheap Hiomant rolls in a range of grits (I start 80, then go to 240) or Hermes J-flex (lovely stuff) for posh. Only use small pieces of sandpaper, in case of wrapping accident!
Finishes (IMHE) are mostly shellac (in tiny plastic drip bottles) or commercial friction polish, polished with wood shavings. Oil on figured timbers first, or waxes afterwards too.
Safety gear is a faceshield (check you can breathe easily without steaming up) and most importantly a turner's smock (easy home made). Short sleeves, no fastenings to catch, smooth fabric and high collar. I don't wear dust protection, because I don't make dust. When I do (scraping, tropicals, sanding) then I do.