If I were you, that is precisely the kit I would be asking for with Christmas coming up. That kit has the correct compound and polish to permanently remove those moderate to heavy swirls and the correct type of pads to work with those compounds for that type of paint condition.
You can't (and I have tried) fugg up that paint with a porter cable and Meguiar's 105. It's pretty much fool proof because if you start to put to much pressure into the pad with the porter cable, it simply clutches and stops spinning so that you can't burn through the paint.
You're paint is in such dire condition that one quick pass with Meguiar's 105 won't make it flawless. You might have to make several passes and take some time working at it, or even find that you might get better results if you were to wetsand first with 1500 or 2000 grit. That kit is capable of removing 1500 grit wetsand marks so that also a good reason why that kit is a good fit for you.