If you’re going to use the chain whip you just made, you’ll also need a way to get that cassette off. A lockring remover is a must-have; unless you use one of the shady removal methods I’ve seen on the internet—which I wouldn’t necessarily recommend unless you don’t care much about the condition of the wheel after you use them. I recommend Park Tool’s iterations here that cost about $6, but you’ll need to buy the specific one for your brand/type of cassette. (By the way, I’m assuming you already have an adjustable wrench laying around somewhere to use with this tool. If you don’t, well, you’ll need one of those too.)
In spite of seat bags’ diminutive size, a lot of people really, really want them to accommodate more stuff. If that’s you, the medium and large seat bag (but not the small) have an extendable gill at the bottom, which you can see in the image up top. It zips open to create more room. With it unzipped, we could cram a wallet, keys, and phone inside the medium as well.
Any bike that gets ridden seriously as transportation or on long rides needs at least a basic tool/emergency kit, and the knowledge to use it, unless the rider is always in a position to call a friend with a car or a cab when their bike needs a quick fix on the road.  If you never travel more than a few miles, this can be overkill, and calling a friend or a cab may be just the ticket,  but if you want to be more self reliant, this is something you should seriously consider.  This list may sound like an awful lot of stuff to carry, but really, it only weighs a few lbs and fits in a small, under-seat bag that comes off quickly so I don’t have to leave it with the bike if theft is a concern.  If you always carry a regular rack top bag, you can also just put all this in a small nylon bag and throw it in there, but I prefer an under-seat bag.
In addition to the Rema patches, put a new tire tube in your kit. The best method for dealing with a flat roadside is to swap out the tube and save the task of patching for later. If you’re not sure what size your tires are, it’s printed on the sidewall of the tire. This inner-tube buying guide has some photos of where to look. What brand is almost irrelevant as many tubes get manufactured in the same place, so whatever your local shop has behind the counter for under $10 will work fine. The only reason to spend more would be to save weight.
Yes, bicycle shops generally provide repair services. A typical list of offered services includes regular service/adjustment (including safety check; and  brake, drivetrain, and tire inspection); premium, and annual service, which is a more extensive tune-up. More specific repairs include drivetrain tune-up, brake system tune-up, flat tire fixes, brake repairs, cleaning and touching up the bike frame.
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.
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