Only time will tell how long any print
will truly last. Inkjet printers have started to produce photo-quality results only within the last few years, so we don't have any antiques to examine.
That said, you can check out the rankings from Wilhelm Imaging Research
, which attempts to simulate how prints made by popular inkjet printers might withstand the ravages of time.
If print longevity preoccupies you, you should probably buy the name-brand inks and papers recommended by your printer maker, despite the sticker shock. Each printer is designed with specific inks and papers to chemically interact.
Learn from the past to preserve the future: collectors of vintage photography come across an abundance of materials scarred by rusty paper clips, tape, and glue. The only thing that should touch your photos is acid-free paper or a UV-protected frame. Safeguard your pictures in an environment free of light, humidity, and extreme temperatures; those kitchen fridge photos are already goners, thanks to so much sunshine and smoke.