I hadn't realized that it was plywood, and I got great advice on how best to finish it.

After a thorough cleaning, I sanded VERY carefully, doing as little hand sanding as possible, and only using a block when I did that. I didn't want to accent the grain any more than it already was. I was able to knock down the grain a bit, but stopped when I was satisfied with it. I removed the formica top, sanded and patched the top plywood, then added a carved trim.

I primed with BIN, then used a satin finish paint to minimize the sheen. I painted the inside of the drawers a pale teal color, then finished with new hardware.

It's still not a great piece of furniture, but it has a new look that better suits our bedroom, and I'm hoping we'll get a few more years of use out of it.

To be fair, here's a pic with flash, taken in the same lighting as the "before" pic:

Thanks again for all of the help!

I used a "Ultra white" paint, which I'm not sure I would do again on such a large piece. It's so bright, stark white, it almost glows! The satin sheen was a good choice, though. I've used it for other pieces, and I've found it to be very forgiving on an imperfect surface, and it gives the furniture a soft glow, instead of being so shiny.

I had never used a miter box or done any kind of trim work, and I thought this would be a good practice piece. I learned a few tricks doing that, too.