Which printer on the market saves you on ink uses

ink use you need to study market available printer specification. It is depend on company country and what you need to print and type of printer.

someone elses

The cheapest ink is convenient122

Cheap ink will fade very fast.
There is so many printers on the market and no one of them is using little or more ink. Just get black ink printer , do not use color.
Or best solution in my opinion:
Print with out Ink, that way you can reuse the blank pages over and over again :)

Best solution is, do not buy any of this electro crap, use print shop service.

Some say that it's cheaper to just buy a new printer that has new ink cartridges in it.

If your printing needs are minor such as a home based PC it is in fact cheaper to buy a new printer once the ink runs out. And yes using black ink without colors is the way to go. I used to work as a customer service rep for HP in London, ON for a few years. They, as well as the rest of them make their profits on the ink, not the printer. This is a strategy that works very well for them. There are numerous sources of aftermarket inks for cartridge refills, and I suggest you try them. HP used to build-in a sensor that would recognize a non-HP cartridge and thus void your warranty, bunch of SOBs if you ask me, but Hey, who is asking.