I'm borrowing this from a site that I used to consult a lot for recipes and that I used to get myself started. You'll want to start off with a variety of alcohols:
- Gin
- Tequila
- Vodka
- Dark or Spiced Rum
- Light Rum
- Bourbon
- Brandy
- Canadian Whiskey
- Irish Whiskey
- Rye Whiskey
- Scotch
Keep in mind that different whiskeys and different rums belong in different drinks. You don't want to get the mixes wrong because you'll wind up with a very different and possibly badly tasting drink.
Here's some liqueurs that you'll find useful if you're trying to broaden your cocktail pallet:
- Amaretto
- Coffee Liqueur (e.g. Kahlua)
- Dry and Sweet Vermouth
- Irish Cream Liqueur
- Maraschino Liqueur
- Orange Liqueur (e.g. triple sec, Cointreau, Curaçao)
- Benedictine
- Chambord (or other raspberry liqueur)
- Crème de Cacao (or another chocolate liqueur)
- Crème de Menthe
- Domaine de Canton Ginger Liqueur
- Drambuie
- Frangelico
- St. Germain Elderflower Liqueur
Lastly, some non-alcoholic mixers:
Juice:
Cranberry Juice
Grapefruit Juice
Lemon Juice
Lime Juice
Orange Juice
Pineapple Juice
Tomato Juice
Other Mixers:
- Bitters
- Coffee
- Grenadine
- Half & Half
- Milk
- Simple Syrup
- Sour Mix
- Tabasco Sauce
- Tea
- Water
- Worcestershire Sauce
Sodas:
- Club soda
- Tonic
- Cola and/or Diet Cola
- Lemon-Lime Soda
- Ginger Ale
You
can get mixers that are pre-made, but they don't taste as good as when you make it yourself. That's because the freshness of the ingredients don't taste as watered down and you have more direct control over how much of what kind of taste goes into your drinks.
Garnishes:
- Lemons
- Limes
- Maraschino Cherries
- Oranges
- Celery
- Cinnamon
- Cocktail Onions
- Mint
- Nutmeg
- Olives
- Salt
- Sugar
- Whipped Cream

Hope this helps.