Hire a K&B designer.

Or do what the rest of us did and start reading. There is a search box at the top of the page and the minimum expected output for someone who is starting out is that they would do a search of this forum to learn about a subject by reading earlier threads. So search on "non-skid flooring" or non-slip flooring and see what discussions have taken place before. It can't hurt to google that, either.

As for your cabinet, the sites mostly all have great search functions for specifying what you are looking for. Do you want wall-hung or free-standing? Modern, Transitional, or Traditional? Doors, drawers, or both? Vessel or recessed sink? How deep? Build.com, Wayfair, Houzz.com, Homedepot.com, AllModern.com (it is part of Wayfair, but just the modern stuff), DecorPlanet.com, SignatureHardware.com and probably a thousand other sites carry vanities. You can get more specific in your site selection by adding a decorating style to your google search. You will not be able to specify 27" at most sites, but will be able to specify a range, like 25-30" or so.

As for a "high toilet," look for one that says ADA on it, then open up the spec sheet on the site (if available) to see the drawing that may show the height to the rim of the bowl or to the seat if it is included with the sale of the toilet itself. Many toilets do not come with the seat. The ADA height has a range, and if you are picky about getting the high end of that range, as I am, you will need to check. ADA height is one of the search terms you will find at the toilet sites.

As for a high toilet you will use a wall mount and set to your liking. That's how it's done.