Welcome. I will start with some basic stuff and others will add to this list.
I would start with getting either Southbends How to run a Lathe Manual, and /or Atlas manual (new from Clausings, cheaper then ebay), some sort of machinist text book that the local school might be using. This will give you a starting point and reference. Machinery's Handbook, any edition from let say 1940s to somewhere in the 80s. Used book store again will be the place to look for, either online or store.
Tools wise. Micrometer, vernier, scales, loupe (magnifier), HSS tool bits ( ignore the carbide stuff and inserts for the moment), dial indicator and base, feeler gauges to help setup the tool height, some good grinding wheels and bench grinder (used to sharpen the HSS tools) a full set of drill bits (preferably US made or better quality imports), Imperial and metric taps and dies will be required in the future. There is a topic covering the tooling requirements here, may have to search for it.
Watch Mr Pete YouTube videos, they are an excellent resource.