Monitoring added after the first incident is monitoring designed by hindsight. This list is ordered so that if you stop halfway you have still covered the most important things.
Before launch
An outside-in check on the thing users do — not a health endpoint, the actual page or endpoint a user hits, with a timeout set near the point a user would give up. A dependency-aware health endpoint, and a check on it, asserting on the body content not just the status code. Notification channels wired and tested, at least two, one of which reliably wakes a person. One named person who gets the alert, not a shared inbox.
Before the first week is out
Heartbeats on every scheduled job, run once manually to confirm the first ping registered. TCP checks on the private infrastructure, so you can distinguish "the app is broken" from "the database is gone." An escalation chain with a human backstop. A status page with three or four components in customer language.
Before month one
Certificate expiry awareness. A restore test for your backups — until you have done this you do not have backups, you have files. A runbook, however rough. Deliberate failure testing in staging: break a dependency and watch what your monitoring does.
What to deliberately skip at launch
Alerting on resource metrics — put them on a dashboard, not in the paging path. Comprehensive coverage — five good checks beat forty mediocre ones. Fine-grained severity taxonomies — two levels is enough at the start. Monitoring staging in the paging path.
The test that validates the whole thing
Before you call it done, have someone who did not build the service pretend to be on call, then break something. Can they tell what is broken? Do they know where to look? Does the escalation reach them? Anything that fails this test is a gap you now know about at zero cost.
The honest bit about ongoing maintenance
Monitoring rots. Put a recurring quarterly calendar entry to walk through the list: are the checks still pointing at real things, do the notification channels still work, are the phone numbers current? Thirty minutes a quarter keeps the whole thing honest.