That is kind of like asking what golf clubs do you need. Everyone has their favorites. I take my home tool box, and a socket wrench set, nothing fancy.
In addition I take the tools necessary to change both the TV and TT tires, including jack, wood blocks, torque wrench and spin wrench. I usually tuck in a small air compressor.
What is important is to practice at home, changing a tire on the road side or in a parking lot is not the time to learn what is next.
Road side service if fine, unless you are on a road two hours from anywhere.
As the scouts say “Be Prepared”.