Keeping photographic prints in good condition for a lifetime is not a simple matter.
Most inkjet photo printers use dye-based inks that will fade and change colour within a few years, especially if exposed to air and ultraviolet light from flourescent tubes or the direct sun, and the ink can smudge if contact with water occurs.
I use and recommend only Epson inkjet printers that utilise pigment inks, not dye-based inks. Epson's pigment inks can last for 70 years or more without fading or changing colour or smudging. In the higher-end printer range, the Epson pigment inks are called "Ultrachrome" ink. In the cheaper range of Epson printers, the pigment inks are called "DuraBrite" ink.
Look for the "Ultrachrome" or "DuraBrite" label when you buy an Epson printer.
Besides the pigment ink, it's important to print on paper that has archival properties. I personally use Epson Archival Matte paper and Epson Premium Semigloss paper. They are rated to last more than 70 years without changing colour or fading if Epson pigment inks are used.
For further information about the longevity of photographic prints, see this website:
Among normal chemistry-type darkroom prints, the Fujicolor Crystal Archive paper lasts the longest - about 45 years according to the above-mentioned web site. In Hong Kong, photo printing shops using the Fujifilm Digital Imaging minilab machines are usually also using Fujicolor Crystal Archive paper. Look on the back of the print for the "Fujicolor Crystal Archive Paper" stamp to make sure.