We sell bluestone tops at our HGTV Home Bassett furniture store. It is a very dense stone and really harder to scratch. You should treat this as a counter top and look into the best sealer / finisher going forward to treat your coffee table.

"look into the best sealer / finisher going forward to treat your coffee table"

And how does that help the op remove the scratches as that was what she asked?

The question is what if it DOES scratch. A stone sealer will help remove minor scratches in natural stone. A stone finisher or polish can also help in removing minor scratches.

I have a tiny etch from some kind of liquid, I'm guessing from alcohol. Do I need to polish it out before sealing? Also what polish and sealer do you recommend?

I would be careful with certain polishers as they may contain a small amount of abrasive matter. These could cause further damage. I would recommend that you use a stone sealer first to see if it helps with the 'etched' issue. I always recommend that you visit your local natural stone supplier to find out more about products you can buy locally and how to apply them.... Good Luck