I've also had some people say "get a browning buckmark" but noone has ever told me *WHY*
The Buckmark would fall in the same neighborhood as the MkII/III or the 22A - a nice, solid 22 semi. Fit and finish is probably better than the Ruger or the S&W, but functionally won't be much different. The fact that they aren't available new in MA pushes the price up here, but if you can get one it will be a nice shooter.
I've shot my dad's Buckmark, I have a 22S and a MkII, I used to have a P22. Haven't tried the MkIII, myself. My P22 was capable of good accuracy, was reliable after some work on it, and was way too small for my hands - sold it, bought a Mosquito, which I'm having a blast with. If you're looking for a 22LR pistol to duplicate a DA/SA semiauto, either one of those will work. They both can be ammo fussy, but are lots of fun.
The Buckmark/MkII&III/22A are all more traditional SA only 22 semis, which are more accurate than most shooters (especially me!) are capable of. They are usually not ammo fussy, and will run forever. Also, lots of fun. I don't see these as in the same category as the P22 or Mosquito, but more target pistol oriented. Any of these would work fine for you - pick by price, or looks, availability, whatever.
My recommendation would be to get the P22 (or Mosquito)
and a Buckmark/22A/Ruger Mk. If you can only get one, I'd stick with the 22A/S or Ruger. When I'm working on accuracy I like knowing that if the shot was off, it was definitely me, not the pistol.