It depends on the hardness of your paint, what pad you use, your technique. I've taken some fairly heavy swirls out of Ford paint with Polish using a DA and a foam cutting pad, that car had about a medium harness paint. Something very hard like VW or Audi paint, you would probably need to step up to UNO or Cut. Only way to tell for sure is to do a test spot. I'd say unless your paint is very hard, Polish should be fine, if it's more on the hard side, go with UNO or Cut followed by Polish (if needed). If you can, I'd get all 3 and be able to take care of anything that comes your way.
IMO, Speed is best used for a one step polish/wax, I wouldn't use it if you were going to use a stand alone LSP.