The one thing missing from SQLite is stronger type casting...however, SQLite does have a solid, cross-platform GUI in DB Browser [0]. It's not as nice as Sequel Pro and some of the commercial clients for MySQL. Postgres, unfortunately, doesn't have near the variety of reliable clients that MySQL and SQLite do.
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.