Last time I was in HD, they had a plain white 60" single bowl vanity top for around $160. They had a beige granite one with bowl for $199, which would be great for resale value. It's super simple to replace. If your vanity doesn't have shutoff valves, just turn off the house water and install them. It's very easily DIYed. If it does have shut off valves, just shut them off, disconnect the flex supply lines, use a utility knife to score between the vanity and top, and lift the whole thing off there. Remove the faucet and install it on the new top, lay a bead of silicone and drop the new top down. Let cure for a hour or two and reconnect the supply lines. Simple.

The people you need to talk to are marble restoration specialists. They have machines that will actually grind a minute layer of the stone off the top, and then bring it back to a polished surface.

Get some denatured alcohol(rubbing alcohol will work for this test) and rub a little on a rag on the finish. If it is shellac, the alcohol will start to dissolve the finish, regardless of age. If the finish dissolves, use the denatured(less expensive than several bottles of rubbing alcohol) alcohol to simply wipe off the old finish. It will take several sessions of wiping. If you want to use shellac to refinish the area, make sure the shellac is fresh(less than a year old) since shellac has a shelf life when premixed. I use a lot of shellac and mix my own in quart amounts(shellac flakes in alcohol, takes a couple days to fully dissolve) You won't need but a pint or so. Applying it as a wiping finish takes a lot longer to get the necessary coverage, but is much neater and easier to control. If the alcohol does not dissolve the finish, try lacquer thinner. If that does not work, someone has used a more modern finish and it will need to be san4ded/professionally removed.

Marble has been used for centuries. Back in the day, it was considered low maintenance. We work in many historic homes and you would be surprised by the condition of the old natural stone surfaces. Restored occasionally (over many decades), and not at a great expense, it is timeless. But our society has changed and with the evolution of new technologies and related products, preferences for the "easy to care for" product have grown in popularity. Yet natural stone will always have its place. If you don't have a water softener, or you have high iron content, these things can contribute to damage to the finish of marble (and other natural stone). These considerations should be taken into account. Of course, today you also need to have a "buyer beware" approach to marble as some of the inexpensive marble is a lower grade, softer product (prone to more issues than the higher quality). While we install plenty of man made tile, the majority of our bathrooms are still natural stone. We do have a higher end client base and for whatever reason that tends to be their preference. We are also in the Midwest and trends are slower to take hold. There are regional differences. While there are a few marble "look a-likes" that are pretty good, most appear fake to those of us who have been real up close and personal with marble on a daily basis for decades. But that's not important to everyone. Obviously it is an individual choice based on the homeowner's lifestyle and tolerance. You need to love your choice for multiple reasons.