Polishing - first time

I have a black Miata, and it’s starting to get a lot of fine scratches. Also, I wrote on the windshield with shoepolish marker, scraped it off, and now somehow the residue is baked all over the front/sides.

Can someone recommend a good product and a good application procedure? I do have a buffer, but I’ve only used it for cleaner/wax, and that was years ago.

wizards compound with the buffer for the paint.

and on the windshield you can use Goo Gone <Orange bottle