I would probably strip the end table with strong (methylene chloride) stripper, because there may be 30 years worth of pledge or other silicone-based polishes there just waiting to spoil your refinishing job. Sanding won't remove the silicone.
Casey

Thanks! I'm sure that at one time I did use Pledge and other stuff. Sounds like it will be a warm weather job!

Stripping won't necessarily remove the Pledge, either. Pledge will cause the new finish to fish-eye (create little craters in the finish). If there is any chance of Pledge contamination, I spray on a couple of coats of dewaxed shellac. While I buy in bulk, you can get it in an aerosol.

Here is a link that might be useful: Bullseye.

You can also add 'fish eye eliminator' to the new finish (it is actually more silicone).