"Six parts gin to one part vermouth" is the final line of the Tom Lehrer song, "Bright College Days," but it is apparently far from the final word on the correct composition of the Martini. From Bernardo DeVoto's perfect Martini that calls for 1.845206 oz of gin to 1/2 oz vermouth and "five hundred pounds of ice" to Hemmingway's ratio of 15 to 1 (both via Eric Felten), this point of contention seems like it can really only come down to your own tastes--and what's fashionable at the time, of course.
Oh, and shaking versus stirring really does make a difference. Shaking the martini both makes the drink colder and dilutes it further than stirring, and even has an effect on the taste. Try both; don't feel pressured by James Bond (he preferred vodka martinis, anyway).
Of the Martini featured in my photos, I know neither the proportion of gin to vermouth nor the method of mixing (though I could probably bug Matt to remember), but I do know that he made it with Hayman's Old Tom gin, which is a favorite of mine (an older style, slightly sweet). Anvil's ingredient list, at least, matches Felten's "Original Intent Martini" recipe: gin, French (dry) vermouth (4:1) and orange bitters.
And in my mind, you really can't go wrong with a lemon twist.
Update: Anvil's ingredients may match Felten's, but Justin would like everyone to know that he uses a ratio of 2:1 gin to vermouth, with 2 dashes of bitters.