Most of the lists are pretty good.
Take something that you can use as a boot. Sometimes you get a small hole in your tire. What you need is something to lay up against the hole so the tube does not ooze out as it inflates and blows up. A dollar bill works reasonably well in this regard and it serves a double purpose of being cash for emergencies.
I much prefer a pump to a C02 inflator. One can run out of C02 cartridges but it is hard to run out of atmosphere.
If you are really conservative a spoke wrench for field truing a wheel and a chain tool for a broken chain can also be used.
The boot, chain tool and spoke wrench are all very rarely needed.