Everclear is PGA (pure grain alcohol) and comes in at 190 proof (92.4% alcohol according to Wikipedia). The more alcohol in a liquid, the faster it evaporates.
It is also consumable so there are no issues of bad residue after it evaporates. Regular rubbing alcohol is poisonous and should not to be used for coil cleaning.
To save money, you can use the cheapest vodka you can find, just get the highest proof you can afford. It's not that vodka wont' work, just that Everclear is better.
ETA: Use the hottest water you can stand to clean the coils, then let them soak in the vodka to hopefully remove or neutralize the taste. Don't forget to clean the tank, too.