Tripoli Powder should give a really fine cut and a way better look to the finish but if you already have obvious lines it won't necessarily delete them. Same for steel wool unless you know what your doing with both. I would avoid Scratch-X most stuff made for cars is made for automotive finishes, not for wood finish.
EEE will be the same as the Tripoli Powder but with a higher gloss due to the waxes.
You need to eradicate the lines before doing anything else.
For what it's worth I've seen a lot of restored antiques with that same marking as what you have and in most instances it comes from shoddy or lazy polishing. The last few steps are very important in getting that brilliant finish you want. Using a cut and polish can help but only as a very last resort.
Worst comes to worst, use some 1500 grit wet and dry on a cork block with water that has a reop of dish detergent in it as a wetting agent. Sand very carefully with the wet n dry and water. This will stop the abrasive from clogging and if done right will get rid of the lines without cutting the finish back too far on the surface of the work. Don't go crazy with it, stop and check the progress regularly by wiping down and allowing the surface to dry.
It could take anywhere from a couple of wipes over the surface with the abrasive to a minute or so, but go easy. You're not sanding just levelling.
You could then use a cut and polish like EEE-Ultra Shine over the top for a higher gloss or Tripoli Powder for a higher slightly dryer shine.