Bummer, I wish people would cover their loads and watch what falls off their vehicles better.
Work with a fine glaze or polish (Don't use anything that says the word "compound" because those usually take off all shine and require massive amounts of work to get the shine back). Work right on top of the fine scratches first, and keep working out so you don't make grooves in the paint or make that area look different from the rest of the door.
For the deep ones, if it is just in the clearcoat, get some clear touch-up paint and fill the scratch with a toothpick or very fine brush one layer at a time till you fill in just above the surface. Then when fully dry, use a tiny bit of 2000 grit sandpaper (glue some to a little wooden block) to sand down the filled in paint only to the surface of the rest of the paint. You will probably dull the paint near the scratch, but then work with your glaze again to bring that back.
For scratches in the primer, you need to put in some color coat and finish as above with clearcoat.
Unless they are REALLY bad, I usually prefer to live with a scratch rather than repaint a panel. Even a very good body shop will have a hard time matching the paint exactly. Sometimes a repaired panel will look OK in one light, but totally different in another light. Sometimes the texture of the paint will differ. But rare is the shop that can make it look 100% like it never happened.
Try filling them in, and live with it for a while before deciding to repaint. You might consider consulting with your insurance company if you have comprehensive, it might be covered if you decide to repaint or have a shop do the touch-up. If you have a shop that can do it right, then go for it if you can't handle the repaired look.
Try not to let a shop take a high speed buffer to the panel to try to fix it, the panel will wind up looking different from the rest of the car and if they aren't very good, they could do more damage. You can do what you need right now by hand.