Best polishing advice I can give is to use the lightest possible polish. An Ultra-Finishing polish is very light, while other compounds will have more "cut". You want to preserve your clear coat as you get the most gloss from your clear coat having thickness.
Meguiar's M205 is very light for polishing the entire car. And with a good set of Lake Country Green pads. After you've finished the entire car, then you can "spot polish" deeper scratches out with a medium-cut compound like "Meguiar's M83 Dual Action Cleaner Polish" and a white pad.
You don't want to over-polish the car. Take it from a guy who is nuts about keeping his car clean and scratch-free. One of the greater problems I created when I detailed my car was that I used too-aggressive of polishes and pads - which cleaned and shined the car perfectly but it took down a lot of clear coat thickness, which lowered the overall gloss and "new car look", even with the car covered in several layers of wax.
If you are new to polishing, it is good to get a good quality polishing kit. Not just some random kit from the hardware store or some Amazon / bang good special. Get something like a Porter Cable PC7424XP kit and a 5.5 inch backing plate and pads - specifically great size and power for working gently on these cars.