DWIW, learn how to use the lathe before starting on any projects, especially for other people.
Beware of thise who say "Can you just…?."
Buy a book or two on latheworki, "Basic Lathework" by Stan Bray, "Lathework" by Harold Hall, " The Amateur's Lathe" by L H Sparey. are all useful aids.
"The Amateur's Workshop" by Ian Bradley is a good book, also.
"The Model Engineers handbook" by Tubal cain is a good reference book.
A set of Zeus Charts, if you don't have them will be usedul for years!
You can expand your library with books from the Workshop Practice Series, on specifgic procedures and tools.
Get used to the lathe and its use by making simple projects, such as A Centrte Height Gauge (A tool that is not on centre height will not cut properly, if at all ), A sliding Tailstock ,Die Holder, a sliding Tailstock Tap Holder, A Mandrel Handle.
These are simple tools which give you familiarity with the lathe and its operatioon, drilling and tapping, and leave you with tools that will be usedul in the future.
You need to learn the ntechnoque of turning the handwheels steadily so as to produce a msteadyn bfeed. OInce the skill has been acquired, you should be able to produce a good finish.
My prefermce is for H S S tools, ,although carbide tips can be verybnuseful
You might find a Tangential Turning Tool a handy tool (If yuou prefer to buy, rathgerbvthan make, the Diamond Tool mfrom Eccentric Engineering inn Oz may suit you. Easy to grind, needing bonly face to be ground., and can be used mfor turning or facing.
HTH
Howard