A wrench that fits the hub nuts: If your bike has quick release front and rear wheels, you don’t need this, but if you have an internal hub on the back, such as the NuVinci, a wrench that fits is a great idea. 99% of the time, this is a 15mm wrench, but you should check your bike. A 6 inch adjustable wrench can also work, but it will be heavier, and when using an adjustable wrench, you do need to take more care to not round over the nuts. A fixed wrench is the best choice. Some multi-tools have a 15 mm wrench built in, but again, if you have limited hand strength, something with more leverage is a great idea.
A pair of disposable latex gloves: Not absolutely necessary, but good for keeping grease and grime off your hands during a repair. Also, nice to have in an emergency when it starts raining and the temperature drops 20 degrees and you don’t have a pair of regular gloves. Just keeping your hands dry and the wind from directly blowing on them makes a huge difference in comfort.
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!
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.