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.)
Mini Pump:   This actually goes on the frame of your bike, as it’s a bit too big for most under-seat bags.   Coming soon, we’ll have a review from Bill of his very favorite one, but a good pump is a lifesaver.    Some people instead carry a CO2 inflator, which is faster and easier to use but does require disposable cartridges, and each time you have a flat, you’ll need at least 2 of those cartridges.  There are combined pump/inflator tools that we’ll also talk about soon.
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.