If I shot only black and white film (with its greater forgiveness) I would give a nod to the classic M3 (double stroke, of course); however, as someone who (as long as it remains available) shoots E100G (formerly a dyed-in-the wool Kodachrome shooter), I would opt for one of the M6 models or an M7, the built-in meter an obvious advantage.
My comments are for the original poster's question. "This is what I'm looking for, anyway... a well-designed and engineered walk-about 35mm film camera.. quick to meter and focus, unobtrusive, with no bells and whistles. Eventually, something my kids will inherit."
A M7 with aperture priority is the camera to consider.
For those reading this post to learn more about Leica Ms.
Years ago I traded my first M6 (.72) for a MP (.72). I'm very satisfied with the MP. Your budget, preferred focal length(s), and meter requirements influence which Leica M to purchase. If money is not a factor consider the MP with its smoother controls, improved viewfinder contrast, center meter dot & improved top plate cosmetics vs the M6 and early M7s.
The M3/M2 has a less brilliant viewfinder with blue tint, lacks the quick-load system, and probably needs repairs due to age. Budget a CLA if you purchase anything older than a M6. The M3/M2 issues may negate their positives.
However, for some, the M3 .9 finder with 50/90mm uncluttered viewfinder is a consideration if you can live without a 35mm frame. A viewfinder magnifier (M 1.25) is available for a .72 M6/7/MP if higher viewfinder magnification is a requirement.
A clean M4 would be my second choice to a MP. You can carry a meter and use a brilliant accessory finder for optics wider than 35mm.
Shooters should save money buying cosmetically imperfect cameras. I confess its a pain to maintain a mint body. No need to get a beater. Buy something nice; add a leather case to cover up handling marks.