SQLite is good choise for absolute beginners.
Later, when teaching "real" multi-user RDBMSes, although MySQL may be more popular, it makes more sense to teach PostgreSQL as "default open source database". Both will do the job, but PostgreSQL has got more stuff right from the beginning, which is especially important when learning. Think PHP vs. Python, PHP may cut few corners but it's not ideal language for teaching generic concepts.
Maybe not even Python, suggest go or rust. My generation we started learning CS with Pascal and moved to C, when we had a bit more understanding.
Rust? NO! One of the worst choices for a first language. Similar to C++, Rust is really heavy on concepts.
Firebird has a more complete support for sql than sqlite has. It also has the advantage of being able to be used both in a manner analogous to sqlite or as a full blown server database.
That being said have you considered using docker (or other popular container tech) for making installation of MySQL easier?
However, SQLite follows most of the standard syntax that Postgres does, so having students move right into CartoDB, which lets you run raw Postgres, has never been a problem.its just the self hosting that's a pain :).
One more thing that I wish I could have from Postgres as a teacher: how it returns an error when you include non-aggregated columns in the SELECT clause. In MySQL and SQLite, selecting extra columns won't throw an error, and the results look close enough to correct to be fairly dangerous for novices. Better to just throw an error as Postgres does.
We (DB Browser for SQLite team) put this one-pager up yesterday about our upcoming "SQLite in the Cloud" project. :)
Hipp based the syntax and semantics on those of PostgreSQL 6.5. In August 2000, version 1.0 of SQLite was released, with storage based on gdbm (GNU Database Manager).According to this, "SQLite was originally written from PostgreSQL 6.5 documentation" https://www.pgcon.org/2014/schedule/events/736.en.html
So, "fork" wasn't the right word. Apologies.
SqLite usually "just works", can easily be reset if you do something wrong (just delete file!) and has better GUI browsers and tools.
I've moved everything to SQLite and couldn't be happier. Not only is it easier to distribute assignments (e.g. a single SQLite file, instead of CSVs that need to be manually imported), it does everything I need it to do to teach the concepts of relational databases and join operations. This typically just needs read-only access, so our assignments can involve gigabytes of data without issue.