The first thing I would do for both the slate floor and concrete countertop is apply a sealer.

I prefer to vacuum rather than use a duster on floors. But for a quick and easy cleanup, a dry swiffer will work fine. I use a paper towel in place of the pricy swiffer cloths.

your slate floor although beautiful, is very porus. your first step is to seal the floor with a commercial sealer. you will need to strip and re-seal a couple of times a year. since the slate is so porus do not use alkaline liquids, they will stain the floor. you can help yourself out immensely by placing a rug down over the area that is used the most. like by the sink. any spills can leave marks on the stone. so be very careful. you can also set some house rules like no shoes on the slate floor. this will keep the traking down. if you are worried about hair on the floor, then yes use a swifter to get them up, but a vacuum would be ideal.the swifter will not clean the floor. you will have to get down on the floor and wash it with some very mild detergent. there are products out there with low ph levels that will work just fine. best of luck