All multi-tools are not created equal, but most with a plethora of features will get plenty of the jobs done. I personally like, and use often, the Lezyne RAP-21 LED tool, which will run you around $30. I like it because not only is it a high quality construction, but it has just about everything you’ll need, plus a sweet mini light. This will give you a chain breaker, spoke wrench, disc brake wedge, and all the most often used Allen keys and drivers. We’re talking a decent number of tools for 1/4 of what they would cost buying them separately.
These are some great ideas, especially the simple ones like bringing a garbage bag. That’s something so easy and cheap that it’s easy to forget entirely, but as you say, it can make a huge difference in the right circumstances. It’s also good that you discuss some minor bike repairs. That’s another thing that can salvage or destroy your ride. You want to be as prepared as possible for the best possible experience.
Change and a $20 bill:   In case your cell phone’s battery dies, it’s nice to still be able to use a payphone if you need to.   Also, the $20 is a great thing to have in case you lose your wallet or have some other mishap.   I’d rather be able to sit in a coffee shop or fast food restaurant when it starts raining while I’m waiting for my friend or cab ride, and a hot cup of tea or coffee or the beverage of your choice and a snack makes it all the more pleasant.  Just try to remember, this is for emergencies, and if you use it, replace it ASAP!
If you are planning on going on a multi-day ride or just riding a long distance in a day, you should have something for first aid, just in case. Unfortunately, almost everyone who cycles frequently will go down at least once in their life. This kit can be really small and compact and can include bandages, some gauze, and a small bottle of a disinfectant.
Basically, you’re stuck with toggling between systems for the advantage of a few pumps, and it doesn’t seem worth it. In the original iteration of this guide, I tested 12 pumps and inflated three different tires completely full to their psi rating, and measured how many pumps it took. Yasuda did similarly for his revamped full-length exploration. That’s 36 tires, and I can guarantee there is no difference between 50 pumps and 100—it’s all terrible.

Now you might be wondering: “I’m carrying a tube; why carry patches at all?” As insurance for the unforeseeable. Wirecutter senior editor Christine Ryan admits she didn’t use to pack them, but said, “I’ve regretted that decision when I’ve had a flat on a ride, used my spare tube, and then, half an hour later, had a second flat. Also, lots of people aren’t very good at figuring out—or don’t take the time to figure out—what caused their flat and remove the cause: thorn, eensy bit of glass, whatever. Then they promptly have a second flat, and everyone else laughs at them.”

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.

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.