Here is a photo for the question above.

chemical: anything that has mass and occupies space.

Sanding off an old finish, particularly a veneered one is rarely a good idea. It's easy to sand through the veneer. It does not remove all the finish. It does not evenly remove the finish. It uses a lot of time and sandpaper. And you might have a heck of a time matching old and new. And most stains need to be applied to bare wood to properly cure. So, for a number of bad reasons, rule that out.

There are lots of options. The link below is the least aggressive. You could pad on some padding lacquer (really a shellac resin) and brighten it up. It may be too glossy for you, but then you can knock it down with some steel wool. Or you can go with the article's wax suggestion.

It depends on how much you need/want the differences in color to go away.

Some people love Howard's Restor-a-finish, mostly people that sell it. I have never found it does much other than a spit and polish over the short term.

Here is a link that might be useful: Saving the finish

duplicate post deleted

This post was edited by bobsmyuncle on Mon, Jan 26, 15 at 17:57

You may wish to check for local businesses that will do the stripping for you. They're equipped to handle the chemicals and can often strip furniture for about the cost it would take you to buy the materials and tools. Refinishing is fairly pricy but mere stripping is usually budget-friendly. You'd do the refinishing part yourself.

they sell a Soy based stripper you could try

Here is a link that might be useful: soy stripper

it really is impossible to tell the condition of the finish. but you have nothing to lose but a little time, by cleaning the surface following bobsmyuncle instructions. then try a little paste wax on a small spot. who knows, it might make you happy.

Thanks for every response. I have read the article you linked, bobsmyuncle, and I admit to being a bit overwhelmed. It seems I have to buy three different products just to tell which kind of finish I have. I do appreciate your expertise, and intend to start with buying denatured ethyl alcohol and checking that first. Tha water marks on the side and some deep scratches on the top concern me most. Thanks again.

I have an update and, of course, another question. I tested the finish and found it was not shellac or lacquer, so I headed off to Home Depot for a finish remover for varnish. I was looking for Bix, but they no longer carry it here in Raleigh. Instead I bought a spray stripper called Citristrip. It is working beautifully and removing the old finish in 30 minutes. The directions say that it CAN be washed with mineral spirits if needed to remove any bits of remaining varnish.
Here is my question: I plan to use clear Briwax, and I do not see any remaining bits of finish, should I still do the mineral spirits wash? I love that the original stain has not been removed, so if a wash is not needed I will move on to the Briwax.

Still OP here, with another check back. I see from reading some older posts that Briwax alone may not be the way to go. Polyurethane also has problems because it can not be readily removed.
I am so very glad that I heeded the advice here and did not try to sand this piece. The veneer is very thin and I would have ruined it.
Here are my latest questions: first, how should I address the places along some edges where the veneer has chipped off? The veneer is so thin that I am thinking of just touching up with some matching acrylic craft paint. If that is advisable, would it be best to do this touch up before the finish goes on?
As to the finish, I have on hand both the no-gloss Polly and the Briwax from previous projects, but I do want this piece to stand the test of time. If I should use some kind of varnish, so that the finish could be repaired in the future, then that is what I will do. Advice please.

Another option is to get a couple sheets of peel and stick veneer, and apply it to a clean surface.

You could fix the veneer chips using wood filler.

Briwax is good but you need to get the colored variety.
In finishing your best bet would be to use a gel stain, and then a top coat of your choosing.