I have learned SQL with Postgres, provided by my university, and found the "explain analyze" and "explain cost" to be a god-send :-) Especially when I was trying to learn the impact of various things on the query-execution time.

When I used MYSQL, I found its EXPLAIN counterpart much more rudimentary.

But if I were to teach somebody SQL, I would probably just use sqlite because it just uses a simple binary file as a backend and doesn't need a running process :)

I am not really OPS or DB guy, so I can't comment on meirts of the databases in production.