For me the bare minimums are:
1. The means to fix a flat
2. The means to ride safely at night
Everything else can be figured out over time based on what annoyances you encounter. I haven't tried CO2 inflators, having always been fine with a little pump. And flats have gotten more rare since I've largely switched to puncture resistant tires. So I'll add one to the list:
3. Consider getting puncture resistant tires when you need new ones
Whether you expect to ride in bad weather is a personal choice, so I'll make these optional:
4. The means to ride in the rain.
5. ... to ride during the winter.