best practice for using system logs

The first file I always check is tomcat-stdout.log. Most of the errors generated by the platform are logged there. If you then need more specific information, you can refer to the Appian documentation to locate a more specific file.

docs.appian.com/.../Logging.html

My suggestion , Don't panic when you can't understand the log ... . From last one year I was into platform maintenance and Manage services so i am giving you most used logs which are helpful for debugging

1. tomcat.std --- The Holy book out of all . It will log almost every action that's going on in your system (Difficult to understand but gives you a idea of where went wrong)
   
   
2. Design_errors - It will gives you a brief about errors (Flashy red messages which end user panics too) that you see in front end 
3. Group Management - Audit of each action performed on a group (Adding/removing users manually or automated)
4. UserManagement - It's for users (Creation/deactivation/name changes etc.,)
5. Site Usage - It will log user activity ,when they logged into site and any following actions like routing to a different page etc.,
6. Web Api Performance logs /integration- when we turn on  trace logs it will audit inputs and out puts
7. log-in /log-out related logs
8. datastore logs - for related call on a datastore etc.,

You can go through documentation for better understanding.