In my experience if you provide 3 or 4 decent cocktails only the douchiest douche won't find something they like.
I think you might be missing the point of this thread.
The point is you want to be able to make 3-4 quality cocktails with 2 bottles of liquor. This will only happen if you spend $40 on mixers, in which case you should have just bought more liquor.
Yep, seems like that's cheap ass is going to get.
For what it's worth, my suggestions are:
Smirnoff Vanilla Vodka
Bacardi White Rum
Along with these get:
Pineapple Juice
Coke
Pina Colada Mix
Strawberry Daiquiri Mix
Orange Juice
Grenadine
With this you can make:
Pineapply Juice and Vanilla Vodka
Coke and Vanilla Vodka
Rum and Coke
Strawberry Daiquiri
Pina Colada
Rum Punch
I wouldn't call this 3-4 great cocktails but it's the best you can do if you are so cheap you only want to buy 2 bottles.