The thumb test is the fine art of pressing on the tube with your thumb to see if it’s inflated. During testing, I took a pressure reading out of curiosity, and to the touch, road tires feel fully inflated around 30 psi. How pathetically sad—30 psi!—when you’re probably trying to reach at least 60 psi on a mountain bike, 70 or more on a hybrid, and it only goes up from there.
Keychain style flashlight or headlamp, LED type, not incandescent:   The keychain style is tiny and lightweight, the headlamp style is a bit bulkier but easier to use.    You can get these for a couple of bucks or less at the local big box hardware store.  The LED ones are lighter, more durable and last considerably longer.   Very useful if you need to make a repair after dark!  I keep a keychain style one as a backup as I normally have a headlamp in my backpack.
More than any other tool in the kit, a reliable lever makes changing a tire easier, especially if you have road bike tires, which are difficult to remove. However, throughout testing, levers seemed to be the one item more prone to failure and poor design than anything else. For example, I found a random orange lever floating around my basement and I threw it in the test pool for fun—it seemed solid enough … until I began prying at the rim of a tire. It bent directly in half, slowly and smoothly, like taffy, and then was boomerang shaped forevermore.
Whether you ride a single, 7, or 10 speed bike or anything in between, you will need a slightly different chain. The major difference is that they come in varying widths to accomodate the different spaces between the gears, but quality of construction is also a factor in choosing a chain. Inspecing the chain should be a part of your regular cycle maintenance procedure- It’s important to keep a chain well lubricated, but oil will also attract dirt and so different oils for specific riding conditions are available. Remember to clean your chain regularly to get the longest life out of it and the gears.