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.
Basic first aid supplies: A few bandages of varying sizes. 6 Aspirin, or other OTC painkiller of choice. A few alcohol pads in sealed foil packs, useful for cleaning grease off grease and grit off of the bike, and also cleaning cuts on yourself if you take a spill. 1 day supply of any prescription drugs you need to take regularly. Wrap these up in tinfoil and tuck away. It might just save your day.
But before I get started, let me share with you a few tips. OK, one tip: Get a work stand. Because putting your bike upside down isn’t good for it—yes, I said it. When I first started fixing my own bikes, I couldn’t afford a fancy $300, folding, magnetic, fixes-the-bike-for-you stand. I tried piecing together a “DIY $30 Stand.” I followed all the directions that the Internet demanded, and once I’d bought all the clamps and pipes, this thing cost really more in the neighborhood of $60—but it only stayed upright with a rope tied to something sturdy in the garage. It was one word: junk. So I bit the veritable chainring and charged a decent stand on my credit card (I hate debt, folks).