Polishing by hand is only going to take you so far if you have swirls or scratches. If you want to use a random orbital, your choices really open up, but your wallet must also.
The Porter Cable 7424XP is kind of the gold standard to start with, but it is slow going if you need to to any heavy correction. The Griots Garage 6" buffer is a very similar machine and will give nearly identical results. A step up from there would be any Rupes polisher and the list goes on and on. Be careful with getting these though, things can get out of hand (buying too many!). I have a Flex 3401 for my heavy correcting, a PC7424 with a 4" pad setup for smaller areas and a Rupes iBrid nano for really small areas.
For polishes, Menzerna, Meguiars, Wolfgang, Adam's and others all get the job done, it is just a matter of preference.
For waxes (protection) there are some choices to make. In order of durability you have liquid wax, paste wax, sealants and coatings. All of them will protect the clear coat, but the polishing beforehand is what really makes the car shine. A nice paste carnauba wax is going to do the most to add depth and clarity to the (previously polished) paint, but a sealant will give you 6 to 12 months of protection while a coating will be measured in years.
I recently picked up an Equinox that lives outside, so I put a ceramic coating on it (both paint and trim) and don't need to worry about that one. My Vette only sees paste carnauba, either Adam's Patriot wax or Zymol Atlantique (it is a sample I was given, there is no way on Earth I'd pay over $1,600 for a tub of wax!). Our Volts get sealant for the winter and then paste wax all summer long, although after using the coating, I'm really leaning to coating the Volts also.
There is a lot of jargon with detailing products and companies will call a product something it really isn't. The Zymol Atlantique is called a glaze, but is really a wax. Zaino is called polish, but it doesn't polish, rather it fills and builds up.
The bottom line is that cars are expensive and need cleaned/protected to last. You are the only one that has to be happy with the way the car looks.
