With the caveat that there are not any one hundred year old prints from modern printers...
Use pigment based inks on an acid free paper and store the prints using archival methods.
Less expensive inkjet printers tend to use dye based inks. They produce amazing prints and the prints can have a long life. But dyes often break down over time (this can be a problem with color prints produced photographically as well).
There are pigment based inkjet printers. They tend to be more expensive and a bit temperamental unless used all the time. Pushing tiny bits of pigment through inkjet nozzels is harder because there must also be a binder. Small hole, grit, and glue is not a recipe for success but the printers do it anyway.
Pigments tend not to break down over time and that's why we can still see cave paintings and other pictographs.
All that said, keep the originals.
Did I say keep the originals?
If not, keep the originals.
The only reason this question has come up is because the originals are still around.
Good luck.