A wrench that fits the hub nuts:   If your bike has quick release front and rear wheels, you don’t need this, but if you have an internal hub on the back, such as the NuVinci, a wrench that fits is a great idea.  99% of the time, this is a 15mm wrench, but you should check your bike.   A 6 inch adjustable wrench can also work, but it will be heavier, and when using an adjustable wrench, you do need to take more care to not round over the nuts.   A fixed wrench is the best choice.    Some multi-tools have a 15 mm wrench built in, but again, if you have limited hand strength, something with more leverage is a great idea.
We focused on tools that would be useful to a commuter—someone trying to use a bike as a functional way to get around town, as opposed to riding recreationally (road biking and mountain biking). That said, it’s a wild and wooly bicycling world out there, and the streets are packed with so many different bikes, all shapes and sizes, new and old. Customizing your flat-fixing kit has advantages over buying a preassembled kit that always contains a tool (or two or three) that’s a piece of junk, or you don’t need. Or it’s missing something you do need. If you build your own kit, at least you know everything works. And you can add only what’s necessary for your specific bike without ending up with stuff you don’t need.
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.