Hi
When I started up domestic cleaning, just used general household cleaning chemicals, pledge, flash etc or unbranded alternatives, cheap enough to buy from supermarkets, stock up when they have offers on. You can get data sheets from the customer care helpline on the product. When it comes to vacuum cleaners and mop buckets/brooms use the customers as this stops cross contamination to other homes, and less to carry around on your route.
No you don't need to carry around a fire extinguisher, but you must have gloves, goggles, dust mask etc, travel first aid kit, accident book etc.
Offices we always made sure if we used their vacuums or ours that they were PAT tested. needs checking every 12 months if i remember correctly.
Hope this helps
Lisa