It is not surprising that a 28 year old vanity tops looks ugly and out of date. I wouldn't recommend repainting it yourself, for the very reasons you are worried about. If you can spend a few bucks, try www.miraclemethod.com. They do this kind of work. Or consider buying a new vanity top. It isn't that hard to replace one, and then you could retire your 28 year old faucet too.
