I use a variable speed orbital polisher. The Porter Cable 7424 (generally regarded as the dog's danglies in the trade) or the Meguiars G220 will offer professional results. Expect to pay in the region of £200.
I bought my machine off Ebay for around £80 (German made). It's crucial it's variable speed, well made, and comes with a variety of cutting pads.
The important part is the cutting pad and compound. To avoid spraying compound everywhere, apply the compound to the foam pad in a cross shape. Then apply the polishing compound to the area to be treated (without the machine switched off). I personally use Merenza 203S (general cutting compound) which provides excellent results, removes fine scratches, hazing, etc. Can be used on fibreglass, etc. It's self lubricating, so with a little experience, you can get professional results. There's a danger of burning, so ensure foam pad is damp and always start on low speed setting. You can also buy lubricating sprays, to assist. I never apply wax with the polisher - this is always done by hand and removed by hand.
My routine: Wash, clay and lubricant, apply Menzerna 203S, buff off with microfibre cloth, Menzerna 85RD final finish polish, buff off with microfibre cloth, and seal with Meguiars Carnuba wax.
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