Logging is your first layer of monitoring. Make sure you understand log levels, log formats, and log aggregation.
logstash is a tool for managing events and logs. You can use it to collect logs, parse them, and store them for later use (like, for searching). Speaking of searching, logstash comes with a web interface for searching and drilling into all of your logs. It is fully free and fully open source.
The most basic metric: can a user access your site / product or not?
Tools to monitor what are your users are actually doing in the product. These are the metrics the CEO and product team look at.
Tools to monitor what your application code, both on the server-side (QPS, latency, through put, error counts) and on the client-side (load time, payload size, crashes).
CoScale provides full stack web performance monitoring, combining server and application metrics, page load times, and custom metrics and events. CoScale simplifies monitoring and troubleshooting with automated anomaly detection and contextual insights, so you can act proactively on performance changes that impact your business.
Tools to measure how the hardware is doing: CPU usage, memory usage, hard drive usage, and network traffic.
More reading on monitoring and metrics
Agility Requires Safetyhttp://www.ybrikman.com/writing/2016/02/14/agility-requires-safety/
To go faster in a car, you need not only a powerful engine, but also safety mechanisms like brakes, air bags, and seat belts. This is a talk that discusses the safety mechanisms that allow you to build software faster.