That is a VERY good video that shows how far you can go down the rabbit hole with inserts.
I found it amusing that he got the best finish (shown at about 27 minutes into the video) with a ground HSS tool and not an insert.? I have recommended that on this group more than once as the best path to a good finish and not use inserts for that.? On larger, more substantial, more rigid lathes using larger inserts, it is entirely different story.
If you don't want to get too involved in the morass of inserts, usually, sources for hobbyists with mini lathes (like Little Machine Shop and ArcEuroTrade) sell a small subset of the universe of inserts that somebody has decided are "good enough" choices.
Surface finish depends on a lot of things, but some of the key ones are machine and tool bit rigidity (not so good on mini lathes), tool bit radius (usually not sufficient on the rather small inserts used with mini lathes), and feed rate (usually too fast on a mini lathe unless it has been modified to be slower).? The "low hanging fruit" to get a better finish on a mini lathe, in my opinion, is to grind your own HSS tool bit with a broad radius.
I have a larger lathe in which I have used inserts a lot.? But almost never in the mini lathe.? Then again, I'm very comfortable with grinding tool bits, perhaps because over a half century ago I was taught that as a fundamental part of learning machining.? On the other hand, it is nice to just pop in a fresh insert (or rotate one to a fresh edge) which is really fast.
Charles E. "Chuck" Kinzer