Quick answer:
Work in this order:

Make it safe
Handle immediate hazards first (electrical, structural, contamination).

Find the cause
Fix the source, not just the symptom, so the damage doesn't return.

Repair from the inside out
Structure and systems before surfaces.

Maintain
Protect the work you paid for.
Where should I start with an old house?
How do I know if there's lead paint?
Is knob-and-tube wiring safe?
Should I remove asbestos myself?