First, centralized logging is not just a good idea -- its key when you start working with multiple servers (which will most likely be almost right away). You need to be able to trace requests / responses / errors across your platform. Many tools (including logging library -> database and a custom log search / viewer) can give you this. Just pick something that works for your budget and development process and start there. To track a single chain of events, you'll just need to have a GUID that you pass between calls in a single request (used for logging).
Next, you'll want to track analytics centrally. Etsy and Netflix have been pioneers in this area. Their engineering blogs are very good to follow. Think: something like a timeseries database (like Influx / Prometheus) and getting data into it. Use tools like Grafana to get data out of it in dashboards or reports. This is separate from your application debug / error logging system.
The next step after this is developing something that consumes data from both of those systems and provides alerts based on unusual activity -- something that provides early warning to devops.
Next, you'll want to track analytics centrally. Etsy and Netflix have been pioneers in this area. Their engineering blogs are very good to follow. Think: something like a timeseries database (like Influx / Prometheus) and getting data into it. Use tools like Grafana to get data out of it in dashboards or reports. This is separate from your application debug / error logging system.
The next step after this is developing something that consumes data from both of those systems and provides alerts based on unusual activity -- something that provides early warning to devops.