The recipes on this site assume that you have a small range on basic ingredients in our kitchen at all times.
Examples of base ingredients are sugar, water, salt, egg white and ice.
We think it's quite safe to assume these ingredients (and a few more) can be found in most kitchens where cocktail preparation is going on.
On the "What can you make" search page, the complete list of basic ingredients are listed in the description at the top.
Most cocktail recipes call for lemon or lime juice, or some other kind of non-alcoholic ingredient.
Depending on your personal taste and favourites drinks your need for juices and such may differ.
For example, tomato juice is not a common ingredient in cocktails, so most people might not have this on hand.
On the other hand, though, if your favourite cocktail is a Bloody Mary tomato juice is indeed required.
So, the best way to figure out what you need to stock up on, is by using the "What can you make" search page and note the number of recipes calling for each ingredient.