Looking at the pitctures there, I think you're likely to be looking at compoounding to remove the marks, but as suggested above, always start with the least aggressive pad combination first and work up.
First off, gently run your finger across the marks - do they catch your nail? Some look like they are down through the colour coat, or it may just be the light. If they catch your nail, then you wont be able to remove them by machine polishing, they will need filled>wetsanded>polished to shift which isn't a job for the faint of heart. If they dont catch the nail, you'll be able to remove or atleast reduce their effect significantly...
As you've noticed, there are a huge range of polishes out there, I can suggest the polishes I use regulalrly but there are also other that will do the same job. Personally I am a fan of Menzerna - I would first of all try Final Finish (PO106FF) on a polishing pad, then light cutting pad. The try Intensive Polish (either PO91L or ideally PO85RD3.01) on a polishing pad, then light cutting pad then cutting pad. If none of this is wroking, then step up to Power Gloss, but be aware that this is a very aggressive compound and by PC will need to be applied using a 4" cutting pad on the PC and followed with Intensive Polish to remove the micromarring. This product is a last resort, only to be used if all else fails!