If you're talking about minimum competency DURING a ride, then I'd say (in order of priority):

1) Fix flat, no excuses for not being able to do this.

2) Fix broken chain - the tool is tiny, and it's really quite easy once you know how. I've never had to on a road ride, but I've fixed many chains during MTB rides.

3) Tighten loose bolts that hold on critical parts. Like the saddle. You can ride without one, but it's not much fun.

4) Use barrel adjusters for minor shifting and brake adjustment.

You can do all that with a good multi tool, a patch kit, and a mini pump. If you ride in MTB shorts with cargo pockets you can fit it all in one pocket.