Good morning!
Wow, 15 posts and no one has mentioned a club yet? I would say, find if there's a turning club in your area, and join. They may have someone that will mentor you and share ideas, let you borrow stuff.
For an example, if you were close to me, I'd let you use my sharpening setup, and you can purchase a mildly expensive (Skip the cheap ones) card hones and hone your tools. Every so often refresh the edges on a sharpening system. I sharpen on my grinders every so often.
Others will have a different opinion.
This could spare you temporarily from buying a system. And it could give you insight if you wanted to invest in CBN wheels, a Tormek or Wolverine. An entirely different argument.
I'll run a pitch for the Tormek. It is by far the most expensive system, BUT, if you get the turning system package, it comes with jigs that sharpen almost everything in your home. Kitchen knives especially. This could make your wife who bought you the lathe happy. (I assume she cooks)... My wife complains when knives get dull. I keep her happy. I sharpen my mother in laws knives too.