Buy a cheapo random orbit machine. It'll make life a lot easier. You can get a 6" one for about 25 bucks at walmart, I've been using the same one going on 10 years now. Probably costs less than just a single bottle of that expensive polish that you plan on buying. Then you can get an inexpensive polish like Turtle Wax Premium Polishing Compound and a synthetic wool pad. That's about as aggressive as you wanna go. I find that the Turtle Polish, followed by
Meguiars professional swirl remover works as a great polishing combo. I don't like scratch x, leaves too much oils and fillers which get in the way of determining the true condition of your paint. Follow it with a pure wax, not a cleaner wax and you'll have a much better finish with way more durability.