The general range for the height of a sink is about 32" to 36" give or take. Vessel bowls vary from 4" to some I've seen that were over 12" tall, so you'd have to choose your bowl then size your vanity to get to your desired final height. An open or closed vanity may depend on the look that you're after. Clean slick contemporary? Something else? The choice really is yours, and the practical nature of available storage does come in to play. As far as chopping down an existing vanity, it depends on how much need to be chopped as well as the style and construction of the vanity. While it's easiest to chop the feet off or eliminate the tow kick on a cabinet, having it simply sit on the floor may look a bit awkward. While more difficult, it often look better to take material off the top, then add a new cabinet top that will compliment the sink. Then doors need to be changed as well. Paint grade you can dicker with, as the primer and paint can hide some scars. Stain grade, it might be easier to just get a new cabinet. Mongo

It will work, but it won't be comfortable and shorter people (especially kids) may have difficulty using it. The rim of most vessel sinks sits ~5-7" higher than the countertop. That's why you see vessel sinks with 30" tall vanities--so the final overall height is right about the same as an undermount sink in a comfort height (36" tall) vanity. Now, if you're looking at one of those really shallow contemporary/.art deco vessel sinks, that may be a different story. Hope this helps!

I considered making a vanity out of wall cabinets. A 2x4 base would be easy. You can find wall cabs in so many sizes it would be easy to get exactly what you want. I am going to use a piece of antique furniture. I have 6 possibilities right here at the antique store. I also have two pieces of my own but I don't want to cut them in any way. Better to cut someone elese's. I'm trying to get away from the miniscule drawers that every vanity has. I will use either a small chest of drawers or a desk looking thing. I considered an antique wash stand but they're really too tall unless I can cut a couple inches off the legs.

My vanity is 33 1/2 inches including the granite countertop. I have a Duravit (ground or grinded)sink on top of the counter. It is 4 3/4 inches high and I find it a good height. I have had no complaints from others and I have never had the water dripping toward elbows problem. Another bathroom has 34" including granite countertop plus 4 7/8 inch high sinks on top of granite. it might be more difficult for small children to reach properly though. I am about 5'6" tall. My DH is over 6'.