First, a decent tool kit. No point in having spares if you can't install them.
Optional - multi-meter, cordless drill and rivet gun.
Extra bulbs and fuses. Hot water heater thermal switch kit (small, not expensive)
As much documentation as you can get. Parts books, manuals, service manuals. Almost all can be down loaded for free as pdf files. You can use a smart phone, laptop or tablet to read them. Knowledge is power.
Money...you can buy most of the parts that break on the road. Airstream uses many of the same parts that are used on other trailers. I've bought repair parts from RV shops, hardware stores and auto parts stores.
Finally, be ready to by-pass, patch or ignore many failures. Heater goes out, get a small space heater. Stove doesn't work, get a camp stove. Hot water out, by-pass the automatic switches and use it manually.
All of the spare parts I carry will fit in a small cigar box.
Mostly, just have fun.