Sorry for the late reply.
It will all depend on what kind of dirt it is. If it's just dirt then a good high alkaline cleaner will do it. Then after a good Impregnating sealer after will help in the maintenance for your client after the clean. Don't forget to pre-wet the stone prior to adding your alkaline cleaner you want the product to work on the surface of the stone and not in it. Agitate it in and allow to dwell 10-15min then agitate again and extract.
But if the stone has previously had any sealer on it or even a wax, then this will need to be stripped as well. If it's topical then do as above but add some honing powder.
All this can be done with your rotary and your brush but you will need to have a descent wet vac as well.
As for product ours are Aqua Mix, Aqua-Seal but others I am sure have others which ever is your preference. I would be happy to set you up a trade account if you wish.
Next your price per m2, this is the most common question I get when carpet cleaners are coming into this business. Every job is different with stone so prices vary it is also down to conditions, masking off, size of area and most importantly what you believe or know you are worth time wise. As a rough guide perhaps £10-15 per m2 maybe even £20.
If you want to discuss or ask any more questions feel free to call me anytime within reason.
Tony
Tiling Logistics
Marble Life Ltd
07584674006