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.)
A multitool is a highly versatile piece of repair equipment that can address most of your maintenance needs. Ideally, you should use it before a ride to tighten and adjust everything properly, but sometimes it’s necessary on a ride as well. If you encounter a loose screw, realize your saddle height is not right, or that your brakes need tightening, you will be happy to have it.
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Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.