Restoring a Craigslist Vanity

Hi everyone! I will be using this thread to keep track of the progress made on restoring a vanity I bought on Craigslist for $30. I will be properly restoring it and NOT painting it. Nothing angers me more than seeing beautiful vintage furniture that has been painted! I plan to start work on this vanity this weekend. In the meantime, can anyone give me a more accurate guess on the year? I know it is 30s or 40s, but which one is it most likely? We have looked in drawers and behind the mirror to try to find a signature with a date and can't find anything except what looks like former owner's names penciled in on the back of the mirror.
All of the drawer pulls are there, but one is broken. I have found a pretty similar replacement on Ebay, but am still looking. I may just end up buying all new hardware. The glass shelf is missing. It seems that that will be pricey to replace.

I'm betting that's almost certainly mid-30's. Good for you for not painting it. It looks like the missing veneer is confined to flat surfaces: LUCKY. That's always the hardest thing to fix without it being obvious, and why so many such pieces end up painted.
Remember that in most cases, refinishing cuts the value significantly. If you can get away with just cleaning it up and waxing it, you're good. But of course, you have veneer to replace anyway, so you're probably going to be all in.
Don't be so sure about the glass shelf. If you know what it's supposed to look like, it shouldn't be all that expensive. And you can easily cast a replacement for missing hardware using the ones that are present, even if in plastic (I wouldn't be surprised if the originals are).

Good luck - anxious to see your progress.