There are cheap bourbons and there are inexpensive bourbons. For something like this, I prefer to use something inexpensive that has flavors I like. I have found that WL Weller is very good whiskey for the price, as is Very Old Barton (though this really needs a splash of water to soften it if you're drinking it straight). Ancient Age, which is on the rot gut shelf, is very tasty stuff. I would not hesitate to use any of these.
I agree to avoid Evan Williams.
Neither Buffalo Trace nor Elijah Craig are on my favorites list, though they are good whiskeys. There are other whiskeys for that price I prefer (Wathen's or Elmer T. Lee) and at that price I'd rather drink it with a couple of cubes.