Well, I suppose one's personal preferences regarding budget, make, dials, age, style, movement, country of origin, etc., all play a part in deciding what to look for. It's difficult to put into words exactly, but I suppose my criteria - over time - embrace:
1. Age: timepieces from before 1970 and preferably from 1930-1960'ish
2. Style: classic or genuine military (not military-style), no divers watches - can't stand chunky bezels
3. Movement: not necessarily heavily jewelled movements, but well-finished, preferably American, then Swiss, then German, then French...
4. Power drive: hand-wound, no batteries, no automatics (too much bother) - but I admire the technology in Solar watches and have one of those
5. Country: American watches, particularly railroad grade pocket watches, then Switzerland
6. Makes: Can't afford posh makes, so good names like Hamilton, Waltham and Elgin (all US, not Swiss versions), Roamer, Gruen Curvex, Wittnauer, Oris, Omega, etc.
7. That indefinable something... chronographs when I can afford them!
And so on! I check European makes against http://www.mikrolisk.de/ which is a rough guide to origin
So, as far as getting the Hamilton, it immediately ticked a few boxes: (1) make (2) year (3) style (4) condition - and I just had to snipe it!