If you want to polish them, you don't have to buy anything special. Any polish will do the job. Depending on how rough the surface is, you can start with anything between 600 and 1000 sandpaper. Finish with 1500 or 2000.

The plastic is soft enough that you don't need compound. Polish will do it. It would go a little quicker if you use some compound, but not much if you use some 1500 to 2000 paper. And don't let the surface go dry. The plastic will burn and smear much easier than paint.

If you decide to polish them, they usually look better and are clearer. But you will need to redo them periodically.

As mentioned above, the best and fairly permanent fix is to spray them with catalized clear after sanding with 600 or so sandpaper. Spray bomb clear doesn't work, it just lays on top of the plastic and looks like fish eye.

We spray the headlights in just about ever car we get in. It is amazing how headlights that are yellow and completely fogged look almost new after clearing.

Either way, it is important to sand the surface enough to remove the oxidation and old sealer.