+1Telling others how to enjoy their liquor is so pompous. Doubly so when the subject at hand is "cheap" liquors.
I'm a hop, skip, and a jump away from the KY bourbon distilleries. I grew up with it being the default liquor choice when you wanted cheap high-octane booze. Bourbon is my liquor of choice.
Typically, if I'm going to be mixing bourbon for cocktails I don't want to use some expensive single-barrel or whatever. I definitely go for the <$20 a bottle territory.
My go-to choices for a cheapy are: Jim Beam black label, Wild Turkey, and Ancient Age.
Ancient Age is bottom-shelf cheap, but is remarkably good. It's not as layered or complex as a lot of the higher end stuff, but sometimes you don't need to analyze every drink you take, you just want to enjoy a rip of booze. I like it straight with a few cubes of ice in it when I just want a quick couple of fingers of booze. As a mixer it's a no-brainer.
Ancient Age is from the Buffalo Trace distillery, and I find that I like most everything coming from them.
+2 on the Wild Turkey for cheapies ... especially the WT 101. Stands up great in a cocktail