What flooring abuts the kitchen floors? e.g., hallway, living room, etc. I ask because that can change your options -- faux wood often looks bad against real wood, but obviously just fine against carpet or tile or other finishes...

We have the original 1.5" 1950's hardwoods in the living room and dining room on either side of the kitchen.

Vinyl Plank sounds like it would be an excellent option for your household. Make sure you're getting a decent quality interlocking plank with at least a a 12 mil. Moduleo, Engage, Karndean, Nouveax, COREtec are all great brands. LVP will do excellent with water in a kitchen, resist scratches great and simple to clean. Making sure it's installed correctly with an experienced installer with the brand you choose is important because if you do have water issues in the years to come, and a board was not properly installed or interlocked water could leak through beneath the installed surface to your sub floor. We've seen this in rare cases but it happens!

I would prefer a stone look with this kitchen. Because there are original hardwoods, the 'wood look' vinyls will have a less than happy life.

There are some beautiful travertine-look, tumbled limestone-look vinyls. As well as vinyl that looks like porcelain or slate.

The place you will NOT find a "good" stone-look floor? A Home Depot. I've seen them. They look pretty cheesy. They've figured out a decent "wood look" product but the stone-look vinyl is pretty bad.

Remember: sheet vinyl has come a long way and is tried, tested and true...and it is truly water proof.