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
Honey Vodka
Sloe Gin
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
Plum wine
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.