GMCfixer,
Of the pistols mentioned in this thread, I have three - a 22/45 MkIV, a Buckmark, and Neos. I might add a supportive shoutout to any of them depending on your priorities. Your first post mentioned "good accuracy"; a relative term, to be sure. Your follow up post mentioned that it's for a young one soon to be "ready" - is that soon to be ready for his/her first beginner pistol, or soon to be ready for entry into competitive shooting? The answer to those questions would also influence my answer to your question.
If we're talking about "good accuracy" in terms of pop can plinking, or hitting a 2-inch shoot-n-see bullseye at 10 or fifteen yards, I'd pick the Neos. It has a smallish grip that still sits okay in my average-sized adult hand, but might be better for a young shooter's hand. It's the most reliable 22lr pistol I've ever had; it shoots anything and everything and never, ever chokes. It can be disassembled for cleaning without tools, although it breaks down into enough parts that I'd say adult supervision is probably a necessity for functional as well as safety reasons. It otherwise meets your criteria - far below the $600 mark (like, somewhere closer to half of that), and adjustable sights, although you'll want to get a $25 aftermarket fiber optic front bead replacement.
If "good accuracy" means good enough for entry level competitive shooting, I'd choose the Buckmark. A more refined pistol than the other two, and in stock form, the most accurate of the three I'm comparing. Very good trigger (especially after the DIY Heggis flip), and functionally reliable, as in, not terribly picky with ammo, but not the 100%-no-malfunctions-of-any-kind reliable that the Neos is. In my locale, the Buckmark is the most expensive of the three, but still to be had for less than $600, usually for less than $500, and sometimes a good deal less.
Somewhere between the Neos and the Buckmark - but closer to the Buckmark end of the scale - is the 22/45 MkIV. Its claim to fame relative to the other two is that it's fabulously easy and simple to disassemble for cleaning - literally seconds to disassemble and reassemble, tool free. More accurate than the Neos and close to as accurate as the Buckmark. A heavy trigger that most experienced shooters don't like (5-6 pound pull, I think??), but which might not be a real detriment for a very beginning shooter (for $125 or so, Volquartsen's trigger kit turns it into a really, really good and crisp 2 pound trigger). I don't think it balances in the hand as well as the Buckmark, but that's a picky observation. It's not so imbalanced as to be a dealbreaker - you have to hold each in a head to head comparison to really notice the difference. I haven't priced a 22/45 MKIV since I bought mine several years ago, but I'm pretty sure they're well below the $600 threshold.
Other than my personal experience with the three above, I'd only add that from time to time I get the itch to purchase a S&W Victory, and all my consumer homework on it says good things, including but not limited to almost universal rave reviews from Victory owners.
Last, I don't see anything that jumps out as a lemon among the recommendations in this thread; best of luck on the choice of pistol!