John,
I use the same polisher that Griots sells, it is great (though you can find the exact same one for less $$ elsewhere on the net, it's pretty common). Do not worry about the bumpers in general, they polish up just fine. Using Griots foam polish pads and Griots polish or 3m's Swirl Remover, you won't harm the paint. For polishing, I use speed setting 4 or 5, and go back and forth over a small area a few times before moving on. I use slight pressure, allowing the weight of the polisher to do much of the work. Put the polish on the pad, put the pad on the car, then turn it on. Never run the polisher without it being on the car, as the pad will fly off. A rule of thumb is that the polishing takes off fine swirl marks and minor scratches. If you can feel the scratch, you won't be able to buff it out.
Absolutely clay the car first, you must!!!. If you don't you could create swirl marks from paint contaminants getting trapped in the polishing pad. Clay by hand, and use a mixture of car wash and water (1oz wash to 12oz water) in a spray boittle to lubricate the paint as you use the clay. If you drop the clay, or a polish pad for that matter, get a fresh one.
Here's a little trick which applies to polishing or waxing: when polishing or waxing the hood/roof/trunk, run the polisher or wax pad parallel with the car (from bumper to bumper in direction). When working on the doors and quarter panels, you want to use a floor to ceiling, or up and down, direction. This helps diffuse the reflected light in a manner which helps flatter the vehicles paint job and styling. The top surfaces (hood, roof, trunk) will "glow" in the sunlight from the light being reflected straight up, whereas the doors and quarter panels will diffuse the light downward, showing off the body/belt lines (which are quite subtle). The traditional method of circular motions was to ensure coverage. You'll get better results using back and forth motions and putting on 2 thin coats of wax as compared to using a circular motion and applying only one coat.
Griots wax shines well and is easy to buff, but doesn't last very long. I'd recommend using the Zaino process instead of wax, but it's a lot of work (4+ coats with Zaino) . However, once you see what Zaino can do, you'll start to enjoy the effort it takes, and you'll only need to do it about once or twice a year, compared to every other month with wax.
Good luck.
-Joe