I think the most important thing is to take care when washing the car, and make sure it has a good layer of wax to protect the paint from the worst punishment.
I always wash the car myself, and then with clean microfiber cloths and lots of fresh water. Cleaning oils without abrasives does a good job hiding light swirls, add a layer of wax and most defects are hidden well.
Scratches and heavy swirls has to be removed by polishing the car, there are many products out there; and I guess other people on this forum can help you much better than I can with how to do that properly.
Btw: I just read your post with pictures of your car, and can tell you that also my car had swirls! I have not yet polished it, but I will have to do it this spring.
For now, I'll just keep it clean and waxed through the rest of this hellish season.