There are a lot of good suggestions so far.

Bike pump - I've had good luck with the Topeak Road Morph. It has a hose, a gauge, and a foot peg, which make the on-the-road repair easier.

I would add tire a boot(s) to the list. Park Tool makes a good one. The boot is used for blow-outs, when the tire (not just the tube) bursts, rips etc. The boot is designed to get you home and not much more, but they do that job admirably.