If you are looking for the cheapest type of whole-home humidifier, then you should go with a bypass type. These humidifiers are the least sophisticated, which means that they are the easiest to install and cheapest to buy. They do, however, require the most maintenance, so you will end up paying a bit of money over the appliances lifetime than you will with other humidifier types.
For instance, while a steam humidifier is the most costly upfront, they are the easiest to maintain. This makes them a good choice as well if you are looking to save money in the long term.