Beer and grape wine are not for me, but I do love a sweet mixed drink.
For classics try
Tequila Sunrise - Tequila, Orange Juice and Grenadine
Gin and Tonic with a squeeze of lemon or lime (mix the drink the take 2 small wedges of either squeeze them into the drink and drop the wedges in as well), I am a Bombay Saphire fan for the gin
My lemonade (7-up for north Americans) mixers, basically these drink go well with lemonade
For a creamy cocktail try
Grasshopper - equal parts Creme de menthe, Creme de Cacao and Double cream, shaken together with ice.
Or for a strong drink, try
Green Dragon - 2 parts Vodka, 1 part Green Chartreuse, shaken with ice
For a very strong drink, try
Absinthe cocktail - 2 parts absinthe, 2 parts still mineral water, a dash of sugar syrup and a dash of Angostura bitters, again shake with ice and beware.
The other direction for drinking is aperitifs, such as
Frangelico, a hazelnut liqueur
Amaretto, an almond liqueur
Lemoncello, lemon flavoured
Going Asian, try
a Cloudy Sake, often drunk cold
Sake, drunk warm
If you are going to get right into cocktails trying to make lots of different ones at home, you will need a large (like 50+ different) selection of liqueurs and other alcoholic drinks. For a less varied attempt I would recommend some basic spirits (vodka, white and dark rum, gin, bourbon/whisky) and several different liqueurs (triple sec, midori, creme de menthe, a nut flavoured liqueur) and some random others based on cocktails you like. You will also need non-alcoholic mixers Angostura Bitter, Grenadine are 2 to always have around.
So there is some suggestion to punish your wallet and liver, enjoy.