Here I am going to explain everything you need to know about the cocktail system in SO:A.

Cocktails are the only upgrades that don't expire after a fight. They last as long as you survive.
They offer different ways to upgrade your character. 
1) The cocktail on the left will always suggest something about buffing your weapon stats.
2) The one in the center - left will give you interesting passives that can save your life.
3) The one on the center-right will give you more unique effects.
4) And finally, the one on the right is the Personal Cocktail. It changes depending on which character you chose. It can always be seen as a safe choice and an easy first pick for people who don't feel like making a choice.

 
The barman allows you to shuffle cocktails up to 3 times as they are randomly chosen. 
So you have space to make the right choice.