Hi there Dave,
I've been cleaning carpets and hard flooring for 15 years, i've just invested in a Numatic 1530 twin speed with solution tank and vac attachement, can also do wood floors with this machine, as far as cleaning vinyls and thermoplastics, regular ammonia free floor stripper is sufficient and as far as rinsing goes I just use a hard floor wand with my portable machine with some acid rinse in the tank to rinse the floor before allowing to dry and apply a couple or three coats of polish, I've never had a problem with this method. Obviously read up on the other types of flooring before doing the work as previously mentioned there are quite a few to get your head round even for us more experienced CC, as I've had to get a chemical set for Dalsouple rubber safety flooring, my first one ever in all my years, but none the less, same principals, just different chemicals, wherever possible, (if in doubt) check with manufacturer before quoting for the work, and if it's your first time at cleaning a particular type of flooring, try and get a sample to practice on and build your confidence, or take your time and don't rush the job.
don't be put off by others, some decent money to be had in the hard flooring circuit, particularly marbles and granites.
Regards
Ralph