What home printer uses cheaper ink cartriges
What printer uses least expensive ink cartriges
the question isn't as simple and straightforward as one might think.
although in stores prices on particular cartridges vary by quite a bit, so does the volume of ink they give you in each cartridge. buying the cheapest cartridge might net you the least amount of ink thus resulting in the same $/vol of ink.
two cartridge systems (1 black, 1 color) will be cheaper to use however if you use up one of the 3 primaries in the color cartridge you will have to replace the whole cartridge (unless you got into refilling your own).
multi-color cartridges are easier to replace and will not waste ink if you print color on a regular basis. if you don't print in color regularly (or if you dont print regularly at all) then you have a chance of ink drying up and having to replace all the cartridges anyways.
the cheapest printer to run would be a laser printer (black and white only). great for high volume printing.