I did not vote due for a few reasons.All are very good picks.
The Browning and both Rugers are very accurate pistols and that's well documented. Even recently in the written media.
I have both a Ruger MK.III and the 22/45 MK.III.
The 22/45 is lighter of the two and has a grip angle, both, of which I like.
The Ruger MK.III sits in the hand a bit more solidly. That is a bonus.
I've had minor experience with the Browning Buckmark, but find it a good sturdy gun. Just like the Rugers.
The Browning Buckmark has a easier take down for field stripping for cleaning.
Rugers and the Buckmark dominate the bullseye shooting matches in numbers present for those who do not wish to plop down a lot of money for more expensive .22lrf match grade pistols.
Since their accuracy is excellent I can see why this is so.
Ruger MK.III pistols can be transformed into more of a match pistol with the adding of trigger assemblies,barrels, and other components from
www.volquartsen.com .
Though there are those who have not had good experiences with the Walther ( and for good reasons) I have seen enough threads for those who like and use the Walther P-22.
So this is a case of what fits you and your needs best.
For example I have small hands and the Ruger 22/45 fits me best for that. Then the Ruger Mk.III. Follow that up with the Buckmark.
For you it very well might be different.
Handle and shoot,if possible, as many of the brands and types you've listed and then go with what fits you and your needs the best.