Agree with what’s been said already, all good advice, especially with some tuition and safety equipment - full face protection masks readily available, new eyes not so.
I returned to turning after nearly 35 years, acquired an vintage record bench top lathe and an Axi starter set of chisels, so as not to outlay to much whilst testing the water so to speak. Essentially confirming it was something I really wanted to get into. I soon sold the bench lathe, (for the same as I paid) it having confirmed that a bench top, whilst good to learn on, I would soon find restricting. After some research, I bought a record power herald which will probably do all I need it to.
I took a couple of lessons at the start, to cover basics, equipment, safety, sharpening etc, all very useful.
If you don’t have a turning club nearby, which I would advocate as your first point of contact as there will be a high level of experience, may be worth checking out your local Men’s Sheds. Both my local ones have a lathe, one has two, but, do check that there is good knowledge there also, ask polite but direct questions regarding experience to confirm your getting proper advise. However, as said already, paid tuition is best option in my view.
The point is well made ref’ what you need to start and how it can easily grow, restraint is definitely required. To see the danger lurking to your wallet, take a at some woodturners early YouTube workshop tour videos, then look at their latest tours to see how stuff has grown. Wish I had !
After the Lathe and turning tools, I would strongly advise to focus on a repetitive sharpening system, as not being able to maintain a sharp edge on chisels will quickly dampen your enthusiasm and can lead to safety mishaps. Yep, you can freehand, and some will tell you it’s the best way, but not for me and a great many turners.
You don’t need anything too to fancy to start, a bench grinder, but DO swap out the grey wheels to cooler cutting types, grey wheels generate lots of heat and not suited to HSS tools, (pink or white aluminium oxide wheels are fine to start) and a couple of jigs that will allow you to quickly repeat the same edge each time with minimal fuss.
I started with my small bench grinder, I purchased the wolverine system, ( approx’ £150, plenty good for me as a start off system, not overly expensive and easy to sell on when I wanted to move up a step. Now use Sorby pro edge.
Apart from the basics, add what you need when you need it. Just a faceplate can get you going, but a chuck will be on your radar very soon and will make things much easier.