Sorry, I don't have any expertise in that area. But we're going to beat you about the head and shoulders for painting it instead of stain and varnish.

 

Andy, I'll come help with the beating. Just let me know when

 

I've read that there is no such thing as a totally waterproof finish there are only levels of water resistance. The most water resistant finish is catalyzed epoxy. It is also the hardest to put on an when it does eventually crack and need refinishing it is the hardest to repair. Oil based varnishes come next. The chemistry of finishes changes all the time so maybe there is one now that won't yellow but most probably still will and although the black should help hide that I think you will still be able to tell a difference.

 

What Charles said, and you'd have to for sure do the vertical edges of the sink and faucet cutouts.
Premium Black FX Poxy Galaxy Countertop - Counter Top Epoxy
Bar Top Epoxy | Commercial Grade Bartop Epoxy

 

The finish on a vanity needs to be splash-resistant, not waterproof - unless you're planning to let the cabinet fill up with water. A good quality satin lacquer should be more than adequate, look at what Sherwin Williams or similar manufacturer sells for finishing kitchen cabinets. Over the years, I've never had a problem with water damage to the edges of the sink cutout or holes for the faucet, a quality caulk job should keep any water from getting to these areas.

Many years ago, in my inexperience, I painted some kitchen cabinets a pale yellow to match the walls and then top coated them with polyurethane - looked good at first, but they definitely started to darken over the years, very noticeable against the painted walls. I would think that one of the new water-based acrylic polys would be a much better choice nowadays as they're not supposed to yellow (and I've added Trans-Tint to them to give a less "artificial" looking appearance to stained parts. There was a very good article in Fine Woodworking some years back covering painting cabinets and some mention of acrylic poly as a top coat to give better protection.

 

I think calking carefully around the openings will give you the seal needed to protect the edges. I would ask at a real paint store what you could use that was water resistant and would give you the kind of look you seek. Personally, I wouldn't use any plastic type coating. Any countertop you might use should keep the moisture away. A wooden top or laminate sounds like a very bad idea to me.

 

" Personally, I wouldn't use any plastic type coating."

Oh ye of little faith!...

(wood+epoxy+water)

 

It had too much damage to the veneer on the top and front so I had to paint it. Trust me, I would have preferred to stain it instead! I rebuilt the bun feet with a weird foam epoxy made for that and I spent about a month sanding and rebuilding it!