Got a mini-lathe for Christmas last year and needed something to put it on. Hundreds of spinning tops and mushrooms later, I’m pretty sure it was worth it. Here’s a couple other things from my lathe.
Truly, the only problem I ran into was imperfect cuts, but it sounds like you have the cutting bit covered. I did like the double 2x4 idea for the legs, made it easy to support the bottom shelf while still be sturdy.
I used 2.5 inch deck screws for everything except attaching the top. Bought some 1 inch corner braces to attach it to the frame.
Best of luck when you build yours!