Simple syrup is your friend. I don’t use a lot of it for myself, but it helps take the edge of some of the more sour cocktails, if you know your company may prefer things a little gentler.
There’s the classic Margarita, on the rocks:
2 parts tequila
1 part freshly squeezed lime juice
1 part triple sec (e.g. Cointreau)
You can tame it a little by adding simple syrup, but my favorite part of a good margarita is its assertive acidity.
Gimlet
4 part gin or vodka (I much prefer gin in this case)
1 part Rose’s lime syrup
I don’t usually like Rose’s, but a lot of people are very particular about Rose’s being used in a gimlet. Instead of Rose’s, you can substitute about 1/2 part simple syrup and 1/2 part (or a little more) freshly squeezed lime juice.
Vodka/Gin Tonic
1 part vodka or gin (I strongly recommend gin in this again)
1-2 parts tonic water
Lime to garnish
Serve over ice with lime to garnish. The lime is an important accent in this drink, so make sure to serve. It particularly goes well with the gin.
You almost have enough for a Long Island Iced tea with rum, tequila, gin. Here’s the complete recipe, as I make it:
1 part each of the five whites: gin, white rum, tequila, triple sec, vodka
2 parts lemon juice
2 parts simple syrup
Splash of coke, lemon to garnish
You can live if you skip the gin or triple sec, although it’d be nice to have the triple sec around for margaritas.
If you want to take shortcuts, you can get stuff like Sour Mix and Sweet and Sour Mix, but I think you’re much, much better off squeezing limes and lemons freshly for cocktails, as these mixes have, to me at any rate, a weird chemically sharpness to them. I’d say the two tricks to really good cocktails are simple syrup and freshly squeezed citrus.