1. Topeak Roadmorph Mini (the full size road morph is a nicer pump but larger and harder to carry so I just bring the mini on my commuter):
https://www.amazon.com/Topeak-Mini-M...dp/B000FICCQC/

2. Replacement tire inner tube (you need the right size though, you can either figure it out from the side of the tire yourself, or take your bike to your local bike shop and ask them for a replacement tube in the right size):
https://www.amazon.com/Continental-P...dp/B01CYTV4OA/

3. Gluless patches
4. Tire levers
https://www.amazon.com/Park-Tool-TR-...dp/B000AO7K0E/

Other thoughts:
- "glue" tire patch kits - I don't like them because the glue tube tends to glue itself shut after it's first use making the whole kit one time use.
- CO2 - no way I'd recommend this to someone who is just learning to change a flat as you do it wrong and you lose all the CO2 in the cartridge. Pumps never run out of air so if you hook it wrong the first time no big deal.