Chemistry - strong as you like on the alkaline side. I use a stripper on really bad ones, and add an oxidiser into it sometimes as well
Agitation - plenty of it. Black pad best if badly soiled, you'll go through them quite quick but cheaper than replacing a brush which is the other alternative.
Extraction - My personal opinion is that using a wet (not dry

) vac and then "rinsing", i.e. mopping water over the floor, is a PANTS way to clean a floor. The only way of properly rinsing to remove all residue is to use an extraction machine - much faster than the other way too. You will need a hard floor wand for sure - safety flooring will knacker a carpet wand in no time, and if you have a glide on the wand it'll wear it out pronto! The little metal bits also lodge in the teflon and make it rough.
Sometimes these floors are permanently stained, the traffic lanes will be permanently grubby looking even after all the cleaning in the world. I would do a test clean first before quoting
