G.B.
I have always used just normal cleaning supplies. I use Comet with Bleach to clean the toilet, tub, sinks, etc...and don not have any problems. We have a garbage disposal and have NEVER EVER had any issues with it. Lots of people say you're not supposed to have one with a septic tank but...oh well. We do and we have never had any issues with the tank what so ever.
I think that you might want to research those enzymes they say should be put in once a month to help keep it cleaned out but we have had the house for over 25 years and don't put anything special in the system.
As for a well, I don't know anything about them.