You don't just want cheapest you need some that last also. Cheap cartridges you need to replace often are not very cheap.
If you don't care about color, get a laser jet, the toner lasts far longer than ink jet ink. If you want/need color, look at this site http://www.cartridgecompare.com/
You should also get a printer that has separate inks for each color so when you run out of one color you don't need to waste the others if they were all in one cartridge.