First, it's important to understand that in order for this to work, you need to keep the water ON TOP of the 2nd floor kitchen. In other words, if you were thinking that you should simply lay plastic down, then install a new floor, what you may end up doing is trapping any water between the PLASTIC and your new floor. And if you have any wood between the plastic barrier and your kitchen floor, well, you've created a potential rotting problem.
My vote says that you want to install tile. Why? You'd use a cement backer board and you can seal up the tile grout. Neither of these are easy to penetrate even when it comes to water. Sheet or Square vinyl has too much potential for problems because of the seams. And I don't like hardwood in the kitchen unless I have $$$ to burn (although it looks reeeeeeeal nice!) The only thing I'd think about with tile is that 1) it's cold unless the floor is heated (from the room below or by underfloor heating), 2) pretty much anything you drop on it will break, 3) you need the proper joist spacing and subfloor to SUPPORT the weight requirements of tile, and 4) tile floors are nice but I've 'heard' that they're harder to sell (it's just what I've heard.)
I know this may sound off-the-wallish but what's the source of the water? I have a 15' x 30' kitchen + 1/2 bath on the 1st floor and no water gets to the basement. We have sheet vinyl (with 2 seams running long way in the kitchen, yet it's no problem. Is the dog knocking over his water bucket like 3'xs a day? Or are the kids using the sink hose as a shower?