A few random thoughts...
The L frame was purposefully designed to duplicate the dimensions of the K frame through the trigger and grip area. The N frame has a slightly larger span between the backstrap and trigger, which can be uncomfortable for shooters with smaller hands; OTOH the smaller K/L grip can be made to feel larger with custom wraparound grips.
The K frames are the lightest with equal barrel lengths, which renders them more "pointable" at the cost of more severe recoil. The L and N frames generally have similar (heavier) weights with equal length barrels, although the L frame will usually be more muzzle-heavy. The reason for this is that most L frame variants have full barrel underlugs, which generally offset the slightly smaller frame and cylinder.
Don't ignore fixed-sight guns; they are arguably more carry-friendly, and generally cost less than the adjustable-sight versions. The fixed-sight K frame equivalents of the M19 and M66 were the M13 and M65 respectively.
The M13/65 seems to have sold better with a 3" barrel than the M19/66, and the 3" barrel is the shortest length that allows a full-length ejector rod capable of positively pushing a .357Mag case fully clear of the cylinder. The more common 2-1/2" guns have a "shorty" rod that can't push a stuck case all the way out- a rare problem if you use good reloading technique, but a potential problem nonetheless.
The SS version of the M586 is (logically) the M686. However, unlike the fixed-sight equivalents of the K frame guns, the fixed-sight L frames- the M581/681- are quite uncommon due to abbreviated production runs. S&W had the misfortune to offer these guns right when many LE agencies started to switch to high-capacity semi-auto "wonder nines" and lose interest in less-expensive fixed-sight .357s.
