I'm a big fan of sours of various sorts. The thing to remember is to stay as far away from sour mix, either at home or in a bar. That is, unless you really want an over-sweetened glass of corn syrup and artificial color...
To start with, for any real mixing, you need to make some simple syrup. Google for details, but you just boil some sugar and water for a minute, then cool. Start with something like 1 cup sugar and 1 cup water... People use different proportions, and in the end you'll adjust the drink recipes for your personal syrup recipe, so just start with that and experiment later. Store this in the refrigerator, it'll keep almost indefinitely, but hopefully you'll use it up before then.
My generic sour recipe is liquor + citrus juice + simple syrup in about a 4:2:1 ratio. For a typical-sized drink, that'd be 2 shots liquor, 1 of juice, and 1/2 of syrup. Pour these over ice (cracked if you've got it) in a shaker and shake until it's cold, then strain over fresh ice in the serving glass. Garnish and go.
The standard sour in the US is whiskey -- I use either bourbon or canadian whiskey. I wouldn't use anything too expensive because you're not going to appreciate the fine points of a single-barrel craft-distilled bourbon in this drink. I wouldn't use bottom shelf stuff, though. Anyway, the whiskey sour is whiskey + lemon juice. Freshly squeezed if at all possible, but you can get a decent drink out of bottled juice. For a garnish, an orange slice and a cherry, or just the orange slice.
Another nice sour is one popular in Chile and Peru: the Pisco sour. Pisco is a brandy from that area (I won't get into whether its Chilean or Peruvian, this is an ongoing dispute). I know the larger liquor stores around here carry Pisco, but I've never seen it (nor looked for it) elsewhere in the US. It shouldn't be expensive-- in Chile you can buy a bottle of the "good stuff" for less than $10 US, and over here it's usually $15-$16. If you can drum up some key limes, those are the best choice for the citrus, but lime or lemon will also work well. This one isn't usually garnished, though you could sugar the rim of a champagne flute and serve in that. In some areas they also add an egg white to the mix before shaking, this gives a really nice foam on top, but I've never tried it and I'll leave it to you to make your own food safety decisions.
Finally, there was a mention of the "Old Fashioned" and "Sidecar" above. Both great, and both have several variations. The Old Fashioned I make starts with an orange slice, a maraschino cherry, a sugar cube, and a few drops of Angostura bitters in a glass. Using the back of a spoon or some other blunt instrument, "muddle" these (i.e., mash up and mix together) until you've got the sugar dissolved. Then add a few ice cubes, a shot or two of reasonably good bourbon, and a splash of soda water.
For a Sidecar, I keep in my head a 2:1:1 ratio of brandy, lemon juice, and Cointreau, but I seem to recall that some experimentation is necessary to adjust that just to one's taste. There's a lot of interesting reading out there on this drink, as it's one of the oldest cocktail recipes around.