If I needed to go into town tomorrow and buy a NIB .22 lever-action rifle, it would be a Henry.
I have owned and used these (does anyone have an exhaustive list of .22 lever actions ever produced?). The ones you can buy new are marked with an asterisk*:
From best to not-best (I won’t use the word worst, none were really bad. Well, the Mossberg, maybe.):
Winchester 9422: Smoothest and most accurate lever-action .22 I have ever used. Beautiful and very well built. I own more than one. They do, however, stay in the safe. (no longer available new)
*Browning BL-22: smooth, not quite as accurate as the Winchesters but the short throw makes it very fast on follow-up; I can cycle it without losing my sight picture. As mentioned, “petite”, which is also an advantage in fast handling if dealing with chicken-stealing varmints, e.g. (you can buy one new for about the price of two Henrys and it might be worth the difference to you if you’re planning to pass it down to the grandkids; time will tell.)
*Henry H001Y (youth model): Smooth and equally as accurate as the Browning for approximately half the price. Can’t prove it, but it may not last as long. Arguably the best $ value out there. (You can buy a new one, made in USA.)
Winchester 250: smooth and as accurate as the 9422 after adding a cheap low-power scope: The factory open sights are among the worst I’ve seen on any rifle; the front sight is plastic, BTW, and I was unable to hit anything with its open sights. Not nearly as well made, was an economy model offered by Winchester but as functional with addition of any kind of decent sight/optic. (no longer available new).
*Marlin 39a: I owned an early model. Very accurate and well-fitted, well-made. I found it to be too heavy and somewhat unwieldy. The action made a “clank” noise which I found annoying (reminded me of another tack-driving target .22 I used to own, a Russian Baikal which sounded like a tank when cycled by hand). They’re both gone now, and, so far, I haven’t missed either of them. (You can buy a new one, but problems have been reported by some)
Mossberg Palomino: Frequent feed problems, accuracy was acceptable but nothing to brag about. Appears even more economically-made than the Winchester 250. I don’t own it any more. (I don’t believe you can buy a new one)
Of the additions you listed in other types of actions, I only have experience with the Remington Nylon 66 and the Browning SA22. Both good guns, you can’t buy a new 66 and the used ones have very inflated prices these days. My 66 broke (split nylon stock/action) and I couldn’t get it repaired.
I traded the SA22 but it was another good “petite” .22 rifle which is offered new by Miroku in several grades, all pricey.
Good luck. You’ve opened yourself up to a lot of choices and, likely, a lot more research before you decide.