Will white chalk paint cover it completely, or give a weathered look?

Do it playfully in color. Update or ditch;) unless you want an equally rather dated Shanby Chic thing

That makes sense Jan Moyer, I'd prefer to update with color rather than make it shabby chic. I like this color, or maybe a grey/grey blue? Glossy or flat, in your opinion? I imagine glossy looks more modernized?

Get a new one this one will never be rustic or modern.

I'd say just get a new one as well.

Also, don't use chalk paint in a bathroom. It is an iffy to bad product to begin with, it can't stand up to wear and tear in a bathroom AT ALL.

I do prefer to get a new one, until then considering a paint job.

idk about chalk paint in bathroom - but had this open already:

https://www.anniesloan.com/annie-sloan-products/paints/chalk-paint/mini-project-pack

If you're going to keep it for now I'd paint is glossy red or the blue you posted above. It depends on what else is going on in your bathroom though. Doing that will give a different, fun look but won't make it really more modern or rustic because of the style. Maybe a white, but I wouldn't use chalk paint.

Limed look:

https://www.anniesloan.com/techniques/using-white-chalk-paint-wax

Houzzer uses Minwax poly:

[https://www.houzz.com/discussions/annie-sloan-chalk-paint-tips-dsvw-vd~3459838?n=27[(https://www.houzz.com/discussions/annie-sloan-chalk-paint-tips-dsvw-vd~3459838?n=27)

Have you changed your vanity yet? Just found this post..I remove the floral appliqué first and give it a quick sanding...paint it a deep peacock blue or navy...add a leather loop handle..I have a lady on Etsy that makes them..they are awesome..will totally change it up..