There are two basic styles to choose from.
Boston shaker: A two-piece shaker consisting of a tin and a pint glass. A separate strainer is required. The Boston shaker is most often selected by classic bartenders and is a personal favorite.
Cobbler: A three-piece metal cocktail shaker with a built-in strainer and a cap.
Hawthorn strainer: A metal strainer designed to fit over the top of a cocktail shaker to strain the drink into the glass. Has 2-4 prongs, and a spring around the outer edge that fits over the cocktail shaker. Controls the speed of the pour while keeping ice in the shaker.
Julep strainer: A strainer that is placed over the glass of a Boston shaker to remove ice and strain the cocktail. Similar in appearance to a slotted spoon and most often used for bourbon cocktails that are traditionally stirred in the pint glass of a shaker.
Bar spoon: A long spoon with a twisted handle used to stir cocktails directly in a serving glass or the pint glass of the Boston shaker.
Muddler: A small club used to crush, mash, or grind ingredients in order to release essential flavors and oils. The muddler is placed directly in the cocktail or pint glass, and it is used with motions similar to those used with a mortar and pestle.
Citrus press: A hand-held juicer designed to extract juice from citrus fruit.