To shake or to stir, that is the question.
No one should mistake me for the cocktail version of William Shakespeare, so you should do that with which you are comfortable. Many people have very firm views on this topic. One obvious advantage to shaking a cocktail is that it gets the libation very cold very quickly, especially if you are using a metal shaker. Also, if you shake vigorously (how else would you do it?) your arms can get a reasonably decent short workout. However, if you stir there isn’t quite the risk of a diluting a cocktail too much with ice.
I am quite aware of my fictional hero James Bond’s mantra when it comes to vodka martinis. Shaking a martini is an exception to the Hamlet Cocktail Conundrum, and it is an exception I embrace. Just figure out which method you like and go with it.