With regard to inkjet printers, the manufacturers have set themselves on a policy of getting you to pay for your printer by paying over the odds for the ink cartridges - if you buy them from the manufacturer! There are two types of cartridge - those which contain the printheads as well as ink (H.P. printers for example) and those which contain ink only such as Epson ones. For my now ancient Epson photo 925 I can buy new manufacturers colour cartridges for about £20, and equivalent ones for about £3! As they are so cheap, I have given up the game of refilling them. I have never used manufacturer's ink for such printers and have always had excellent results. As I write this, my trusty Photo 925 is rolling off my daugher's holiday snaps in excellent quality.
The problem with HP type cartridges is that the print heads also have a limited life which is why they are built into the cartridges so they are automatically replaced when the ink runs out. In my experience such cartridges can successfully be refilled with the correct ink (easily obtainable) and the print heads will last for at least ten refills provided you don't let them run completely dry, however I have had trouble with "re-manufactured" cartridges for this type of printer. I therefore start off with a brand new manufacturer's cartridge (ouch!) and then refill this as required.
P.P.