Shaken vs Stirred
There is quite a difference in how the drink finishes whether you shake or stir it. When stirred the drink is perfectly clear, when shaken it has a sparkle to it caused, I understand, by tiny fragments of ice. Some of the high end cocktail bars I've been to prefer stirring – I usually ask for it how it comes and watch them make it. There probably is a difference in taste, but I'd say they are just a little different to each other.
Quinnine is available as a poweder that can be added to try and recreate the trueVesper. Not tried this personally.
I don't recommend you use the Martini brand, Dolin or Noilly Prat are readily available and are superb, costing very little more and as you use so little cost is not that important.
My recipie is to take a large 350ml martini glass and fill it with ice and leave to stand for a minute. Put three shots of spirit** in the shaker, add ¼ – ½ shot vermouth then pour in the ice from the glass. Put the lid on and shake like buggery until the shaker is ice cold a frosted. Carefully strain into the glass. Take 1” of thin lemon peel, twist over the glass and drop it in.
Enjoy and repeat until the world is too blurry to make another one.
** Gordons is great, as it Tanquary Ten. Some people like Plymoth, it's a bolder flavour.