Hi, John,
Welcome! Are you a pirate :?:
It is well worth spending some time considering and looking at the options for all the bits of kit you will need to get started. (Keep saving in the meantime!). In addition to the lathe and tools you will need a suitable bench grinder, chucking systems, face protection and dust masks, abrasives, sealers and polishes, etc., etc. As Jim says, the list is endless, and as you get into turning your list will quickly grow.
But don't be put off - it's great. When I first started I spent maybe 12-18 months researching what I needed/wanted by reading mags. and catalogues, and visiting shows and exhibitions where I was able to talk to and glean good advice from some of the well-known woodturners, all before I actually bought any kit - time very well spent, I learnt a lot, and it thankfully avoided me making expensive mistakes.
If you can get hold of a copy of Issue 146 (April) of Good Woodworking magazine there are some pointers in there on putting together a 'start-up' kit. Best of luck.
Trev.