It will be important to gather all your supplies before the first day of potty training. Most of these you can use for both at home and when out of the house.
For home:
A small potty and/or insert for the toilet - learn more about this here
Cleaning supplies for accidents - consider products needed for all types of flooring
Wipes
I like these for cleaning my kid's legs/feet after an accident
Baby wipes for after poop, as they clean better (just don't flush them!)
Accident protection for couch(es) and bed - I personally like these
Plenty of your reward of choice, if you're using them
Enough underwear and clothing to change into after accidents
For the car/out and about:
A small potty - in case there isn't a bathroom available, or if your child isn't ready for a different toilet
Cleaning supplies for the potty and any accidents that might happen in the car
Wipes
Wet/dry bag - I keep my kid's clothes in these, so I can take the clean clothes out and put the dirty ones in, and then just wash everything at home