stain and refinish
I am by no means a professional woodworker or finish expert but....
I used aircraft stripper to remove the thick outer paint. A plastic scraper pulled it right off after 10 minutes of time. But that left a white layer of primer or sealer. That required acetone to remove. MEK would do the job as well both can be found at home despot et al. Wear gloves work in ventilated area etc.
I suggest not sanding but using steel wool to remove any small bits of white. This will take a long time be patient if you sand you will lighten the wood and damage the grain. I am not sure if it is poplar or maple that the aprons are made from. I used a minwax stain (maple) applied let sit for 5 min then wiped off. 3 coats should be good to seal that wood. You can tell when the wood stops soaking up the stain. I then applied polyurethane one coat per day for a week. 00 steel wool in between to knock down any bubbles and give better adhesion.
As for the plywood sections if yours was delaminating like mine, peel off the outer layer with a scraper, this will leave a nice surface to paint your color of choice, them multiple layers of polyurethane for a nice shiny finish.
I took my time once stripped and peeled to bare wood, paint the black laquer first day and then stain opposite days for a week. then one coat of polyu a day for a week.
For the plastic skirts, I sprayed them with a plastic adhesion promoter you can find at auto parts stores, Then sprayed one coat per day of automotive grade black gloss. I only did the outside face while on saw horses, I should have strung them up and hvlp sprayed them.
One last thing, replace all those screws with new ones. I have a ball return which is rubber coated. My rubber coating was near perfect. If you need to fix that coating you can scrape all of it off and get some thin walled silicone tubing - it comes in a variety of colors,cut to length, slit it down one side and wrap the exposed rod. This would make a nearly silent ball return from foot to head of table.
Good luck - its your table make it what ever color scheme you like.
Next up polishing the metal.......