I don't know of any cordless machines. But entry level polisher would be a Meguiar's G220 and top end a Flex XC 3401 VRG.
The Megs machines is a dual-action RO, the Flex on the other hand is gear driven and has a forced rotation. That means, no matter how much load pressure it won't stall.
These are specialist machines. You can find sander type machines at places like Bunnings. When shopping you need to check the stroke length. This is where you'll get your power for swirl removal. The machines above have an 8mm stroke. You'll find some machines (like I think Ryobi has one) that has only a 4mm stroke from memory.
Ah ok. Yeah the one of the Bosch units is what people usually buy. I'm not sure of the model. It will remove swirls. You'll just need to be patient and do multiple passes on each section.
Either way, 1000 000 times better than hand polishing!
As a total noob to this, am I correct in saying that you use a back and forth motion in a straight line and not a swirling motion? Did that make sense??
Machine Polishing - you work section by section doing like a cross hatch pattern. So you'll go up and down until you work your way across the section being machined, then you'll go left and right working back up the section being machined.
Hand Polishing - Start with circular motions but always finish with straight back and forth motions before buffing off the residue.
I understand what you mean, although you may not have understood me! In other words, straight lines up and down, then left to right, no circular motions with the orbital.