The advice I give to people is "think about logging like a feature with customers, just like any other feature." If you think about logging this way, you ideally put yourself in the position of your logs' "customer"- a bleary-eyed teammate who just got paged out of bed at 2am, or a security guy who isn't intimately familiar with your code. Providing extra context for those users is really kind, as they don't have a "secret decoder ring".
Since the article discusses it, I also highly recommend AWS CloudWatch logs. It's super easy to log to CloudWatch from Lambda with the Python logger class. It's a little harder from EC2, but not really that difficult. The advantage is that you don't need to SSH somewhere and navigate to a file and then locate the interesting stuff in that file - You just keep the CloudWatch console open (or keep a link to it handy) and the latest stuff is on top with easy filtering.