Most "field repair kits" contain parts you can't replace "in the field". If you can't change the part with nothing more than the items in your pocket, sitting around the campfire after supper, it is not "field repair".
100% in agreement with Nate above.
Military armorers do not have time to "fit" parts. The M16/AR-15 is designed to work with the parts as-is. If anything needs fitting, something is out of spec.
A complete new bolt is good to have, is quick to change
I keep in the trapdoor grips of my AR's:
Firing pin & retainer ("cotter pin")
Extractor, pin, spring (make sure you have the silicone rubber insert)
Gas Rings (or 1pc McFarland) (2 spare sets)
Hammer spring
Trigger spring
Disconnector and spring
Hammer/Trigger pin (same pin fits both)
Cam pin
Most of these parts seldom break, but they are small, light, cheap, easy to replace.
A bullet tip, nail, small punch, are all you need. I keep my "universal field armorer's tool" with my AR's... an ordinary Stanley carpenter's nail set. You can adjust front sight post, swing down the trigger guard, push out trigger and hammer pins, remove mag floor plates, etc.
Having good mags is numero uno. USGI's, black or green followers, I don't care. Good springs a must. If you bought the mags used, replace with fresh springs, preferably +10% springs, but good GI replacement springs are OK.
A GI cleaning kit, patches, and a 4 oz bottle of Break Free, a can of Gun Scrubber, and you can clean your rifle in no time flat. At the least, you can flush and reoil the upper and bolt carrier.
Lay in some spare chamber brushes. They are cheap, buy $10 worth. Cleaning the chamber is more important than cleaning the bore. At worst, a dirty bore is less accurate. But a dirty chamber will cause stuck cases.