I'm basically looking for something self-hosted or cloud-based where I can easily POST some data from Python/PHP/JavaScript/Bash running on two or three servers and easily have a look at the logs streaming in.
Spinning up an entire Graylog seems overkill in order to log a couple of dozen lines per day.
Have a syslog-ng running locally on all your hosts and forwarding logs to a central one. Applications can easily send logs to syslog, all languages/loggers support it.
The central syslog can listen for remote logs and save everything into /storage/hostname/year-month-date/file.log for example. This allows you to grep everything from that host.
It's simple and it uses very little resources.
is pretty good for structured logging. But as always: depends on your needs especially with regards to indexing as loki stores only the raw log data and set labels.
But putting new data into it via POST is pretty simple https://grafana.com/docs/loki/latest/api/#post-lokiapiv1push
https://www.honeycomb.io/pricing?
You can set up with one of their Beelines, or just send JSON to the REST endpoint.