The old coat of solid stain that has weathered makes a good prime coat if it's clean, dull & dry and is a sound coat, meaning not peeling or compromised in some other way. Duration is a house paint, whereas the other is a stain. The chief difference is the dry film thickness and sheen. the thin dry film makes the stain follow the contours of the wood and can give you a more authentic or maybe even rustic look, depending on the wood. It will almost always be flat, with no shine at all. The thicker coat will more fill in the grain of the wood and probably have an eggshell or higher shine, maybe even to a satin or semi-gloss. It most likely will not be available flat. A thinner coat means shorter life, the trade-off reflected in the price. A properly applied thicker coat of duration can be expected to last a good long while, but I wouldn't use anyone's "lifetime". If the wood has roughness or character to it, that you want to exploit for a certain look, I'd put stain on it. If the wood is smooth, almost shiny the way it is, I'd use house paint.

What do you mean by stained? Zinsser makes a waterproofing paint that is good for painting concrete block.

Well, you cant remove all the paint, but, you could repaint again with a flat paint or you can go over the paint with a solid color stain. I would not be very happy, if I had said, stain, and my painter used paint. Once its painted, the only way you would ever be able to use stain again is to strip the entire house, and that sure sounds like a whole lot of work. No priming and not fixing things that needed repairing wouldnt make me very happy either. Satin paint is much easier to keep clean than flat paint, but, satin paint also shows all the imperfections as you found out.

Since you're keeping your existing vanity you should post a picture of it and the other finishes in your bathroom in order to get the best advice. But gray is probably not a good choice. Blues are actually more well liked than gray, but I agree with @arcy_gw that white and natural wood are the most popular finishes. I have a white vanity with a white top in my secondary bath that is over 25 years old. It does not look trendy nor dated and it is very low down on my list of priorities to be replaced.