Don't think about this as an irreversible, forced-choice decision. If you buy just about any watch preowned, for a fair price, then you can always sell it without getting hurt too much (compared to buying it new) and get something else. If you're thinking about all 3 of these watches very seriously, then there's a good chance you'll own more than one of them at some point -- just maybe not at the same time, depending upon your financial situation and other preferences such as keeping the collection small.
I love the Lange 1 (especially the older movement -- more aesthetically attractive than the current movement, in my opinion). I've never owned a Breguet or VC, but I've always liked certain models of the Breguet La Tradition. The VC American 1921 never did much for me (though I like that the very first pieces released 100 years ago were for people like me who wore their watches on the right wrist!). Also, the movement-to-caseback ratio on the display backs of the larger 40mm versions of the Americans is way too low for me and would be a dealbreaker -- makes the movement look far too small for the 40mm case -- though movement-to-caseback ratio on the the 36.5mm version looks just fine. As an aside, I've been enamored with the VC Historiques Triple Calendrier 1942 ever since it was introduced. That's a watch I've often looked at.