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.