Deep scratches in the paint after dog (brother-in-law) attack

Hello dear people, I have a serious problem. After a dog attack and after that the tracks (Matsch) my brother-in-law tried to wipe dry the car looks like this from my wife. I asked today what this should cost to polish up was the answer between 500€-600€. That is too expensive. My question would be if I wanted to polish up myself, it would of course go with investment (polishing machine, polishing paste, etc.w) and which polishing agent would be best suited for this. ? There’s just too much on the market. Greeting fantaboy