Of your choices (Buckmark, Single Six), I would get the Buckmark.
I have 2 Buckmark Bullseyes (7 inch fluted barrel, adj sear, trigger stop ). Good out-of-box. Only adjustment I made was sighting in.
Also, look at Ruger MK series pistols, also. Both my Ruger MKIIs (5.5 bull and 7 flat side barrel) required trigger work. New trigger, sear, grips.
Both Ruger and Buckmark are accurate and reliable with Federal 550 bulk ammo. Both shoot better with better ammo (Fed #510, #714, Automatch, etc).
- had a .22 conversion for a 1911. Sold.
- had mouse .22. Sold.
- had a S&W 617 4 inch. Had timing issues. S&W fixed it free twice. Sold.
- have S&W 41 - beautiful, accurate but SV ammo is not cheap so I seldom shoot it. ammo sensitive.
In all, If .22LR , then Buckmark or Ruger MKXXX 5.5 barrel or longer are the best buys.