On the 'accessories' side of the lathe, I too quickly saw that my meager budget could be swallowed whole in an instant. However there are ways to limit the spending - assuming you know what you want (to turn).
Given that you don't have lathe experience, how could you know that? The advice of finding local turners to provide a tour, some advice, and a spin is the best advice - BEFORE you purchase. Or take a class (once we can be close enough to do such things). Or the traveling loaner lathe that NCWW has - may take a while to get that though. Either way you'll get a feel for the types of things you like to turn. Spindle or pen turning, for example, does not need a chuck.
I have a mid-capacity lathe (16"), purchased used, and while I might love to have a top of the line model, I can't justify it. I started with a cheapo set of tools from HF to get my feet wet, figuring that I'd learn to sharpen on cheaper steel (not that I recommend this strategy - cheap tools don't really sharpen well, and
sharp tools are necessary for safe turning). I added a decent bowl gouge, which is what I use for 90% of my turning (because I like to turn bowls).
I sharpen on a stationary belt-disc sander (that I already had)- with a home made jig for turning a fingernail profile on my gouge. Works great (for bowl gouge, ok for other tools).
I consider a chuck (yes I only have one) to be essential for enjoyment (of bowl turning) - although you can certainly get started without one. I have a Nova G3 chuck, which is about $100-120 when on sale.
So for me
a lathe, a bowl gouge, and a chuck were the essential purchases. Realize that there is sooo much more that can be done with more and varied tooling. Also realize that buying new tools doesn't make you a better turner (practice, practice, practice and use good technique) - although things can be done more easily with a broader range of tools.
I enjoyed books by David Ellsworth and Richard Raffan (I think that is it). On YouTube there are many examples of what not to do - but I can recommend John Lucas (john60lucas)
john60lucas
and Lyle Jamieson (on sharpening woodturning tools)
So your budget CAN be eaten up by accessories, but it does not NEED to become an expensive habit to get some enjoyment and produce decent turnings.