I think you'll find that most of the people posting here all walk around with certain items, all the time as a matter of habit. Most will also have one or more kits prepared and ready to go, at home, in the car, etc. Most kits are probably tailored to what they expect that they might encounter, often in a worse case scenario, to the resources they will expect to be able to draw on, and to what they can carry. Look at some of the commercial kits or kits that others have posted about, and read what people say about them.

I like to back things up on DVDs and store the information elsewhere. For example, make a DVD and send it home from school.

My most basic first aid items are rolls of athletic tape, gauze and something that is a topical antibiotic.

Fishmode, that bike should be fairly easy to fix. Bikes are simple machines, except for maybe the modern shifters. You refer to the main bearings, not sure what that means. Is it the bottom bracket through which the spindle for the pedals turn or the ball bearings inside the hubs of a wheel?