Let's start at the top.
Yes swirls are fixable, you can do it by hand but it will be hard. I would get a DA polisher.
So what da would I get? If you are going to do just your car this once, then spread wax once or twice a year then get the harbor freight. Personally I would look for a used porter cable. If new and not the hf unit you can't go wrong with the Griots Garage 6"
Griots Garage 6 Inch Random Orbital Polisher FREE BONUS!. The nice thing with the GG machine is the lifetime warranty. It is more powerful than the hf and pc machine yet safe and realisticly worry free. A dirty pad can ruin the paint, but you shouldn't burn the paint. I use this machine for my business, in fact,I just bought their 3" machine last weekend on Autogeeks 25% off sale. Skip the 6" backing plate and 6.5" pads and get a 5" backing plate and 5.5" pads, either boss
Griots Garage 5.5 inch BOSS Foam and Microfiber Pads Or lake country thin pro pads
Lake Country ThinPro Foam Pad System 5.5 Inch. I have not heard good things about the pads at hf. They may last once or twice, but will come apart from the Velcro backing.
So, what pads would I get? If lake country 2-3 orange, 2-3 white, 1 black. The black will be for your last step, the orange for more severe defects, the white for less. If the boss pads, 2 micro fiber, 2-3 orange, and one black. One of each color won't be enough. There are some cars I use 7 or 8 pads just removing defects.
Next the products you linked. Unless I missed it, I don't see a polish. What you linked is a sealant and a wax. Many people like both of those products, I have never had fantastic luck with Chemical Guys, but have heard good things about jet seal. You need a polish, I looked and didn't see a polish in their line, but Meguiars Ultimate Polish is really good and easy to use. If you want to keep the jet seal use it, wait 15 minutes, and apply another coat. Then apply the Petes. Here you will need another finishing pad on top of what I recommended above, like a red one.
No that buffer you posted isn't going to do anything but make the swirls worse. It doesn't have he power for defect removal, and may have enough power to spread wax, but I wouldn't use it.
I understand this gets expensive fast. My other recommendation is find a pro, pay them $150-200 for an exterior detail. Let them get the car perfect, then you just maintain it. You seal it twice a year even by hand. Get a spray wax or QD, after the car is washed but still wet spray one panel at a time and dry it with a quality mf towel, you should be good.
