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.
A two-stage hand pump tries to marry the best features of both types of pumps: the quick inflation of high volume that can achieve the higher psi ranges of high pressure. But to steal a quote from our floor pump guide, “You pump eight times or you pump 10 times—what does it matter?” That’s a quote from Daimeon Shanks, who at the time was a mechanic for the Garmin-Sharp pro tour team—that’s right, Tour de France, baby.
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.