I find that all I need is 25ml and 35 ml measures, a 500ml shaker and tea strainer or equivalent. You will be able to make virtually anything with that plus an occasional 'loan' of some common kitchen equipment. I would say, give the main attention to the ingredients and the measuring, and all will be well.
Noel Coward's recipe for the perfect dry martini -
"Shake a large measure of gin over ice until very cold. Point the shaker in the general direction of Italy. Drink."
My recipe -
4 x 25ml gin, 1 x 25ml dry vermouth. Shake over ice. Serves 2. My preference is for an 'Old Tom' gin (Haymans or Crabbies) and Dolin vermouth. I don't care for Martini vermouth despite the name. Serve with an olive or, for a 'Gibson', a cocktail onion.
Enjoy. Remember to stop drinking, BEFORE breathing ceases!