A pair of disposable latex gloves: Not absolutely necessary, but good for keeping grease and grime off your hands during a repair. Also, nice to have in an emergency when it starts raining and the temperature drops 20 degrees and you don’t have a pair of regular gloves. Just keeping your hands dry and the wind from directly blowing on them makes a huge difference in comfort.
Broadly speaking there are two major wheel sizes – 700c for road bikes and 26 inch off-road wheels. However there are a whole variety of older, less common wheel sizes and of course fold up bikes have much smaller wheels altogether. Repairing a puncture is not an emergency! It’s a basic procedure that every cyclist should be able to to perform, but doing it correctly involves more steps than many people realise. Wheel building is often seen as the most artful skill in bicycle maintenance, and separates the professionals from the amateurs but that doesn’t mean you should consider it out of reach. Truing a slightly misaligned wheel is a cycle maintenance job that almost any cyclist can perform.