You have a lot of decent options. You could do a lot worse than ELK. If you're on AWS, you can get hosted Elasticsearch. It comes out of the box with Logstash you can hook up to DynamoDB, and it also does Kibana out of the box. There are a number of other vendors; but there are decent reasons for keeping your logs as close as possible.

CloudWatch works fine too. CloudWatch comes integrated with AWS services out of the box. It can be more annoying to get your logs into it than ELK (the latter seems overall more popular). Its alerting and the AWS CLI integration pretty slick, though.

You should also go turn on CloudTrail right now. It lets you automatically log side-effectful API calls. It is not a replacement for a centralized logging pipeline, but it's great high-signal data to put into one.

I appreciate that your complaint (totally valid!) was "this is a rabbit hole", and I just gave you two options, and that might not help your perception that it's a rabbit hole. If you find yourself paralyzed by choice, either choice is much better than deferring the choice! Just pick one. Heck, if you can't pick, let me help: pick AWS hosted Elasticsearch.

A lot of people (also in the security space) like Splunk. I find it annoying to deploy (I've heard rsyslog-in-front-of-forwarders as a canonical deployment method for just ingesting syslog more than once because reasons) and overpriced. YMMV.

Disclaimer: shameless plug! You're not the only one with your hair on fire. One of the first things we're doing for Latacora customers is setting up a centralized logging pipeline.