You often hear PostgreSQL enthusiasts argue that it's a "real" RDBMS, while MySQL is not. This kind of snobbery is dangerous for newcomers, because it comes after years of specific experiences that rub a certain way against a certain personality type. If you want to approach it in terms of what knowledge would benefit a beginner the most - you're far more likely to find people using MySQL out in the wild than PostgreSQL. Big sites built around open source software choose MySQL over PostgreSQL by a wide margin.
Personally, I like MySQL because it fits my development style - it just gets stuff done. I don't use foreign keys. I definitely don't use stored procedures. But what MySQL does, it does well and it does fast and it does it while giving me a happy "okay, that makes sense" feeling that I don't get with PostgreSQL (I've used both extensively). There's good community support for MySQL and excellent documentation. And if you need to do replication (and who doesn't?) MySQL is the clear winner, no questions asked.
There are some things that MySQL lets you do that could possibly lead to bad habits if you switch to less-forgiving databases. But that's the thing - there's all this talk of how you need to be prepared to jump from RDBMS X to RDBMS Y at a moment's notice. In my experience, this happens rarely, and when it does there are always quirky differences from one database to the next. MySQL is different from PostgreSQL, which is different from Oracle, which is different from SQL Server, which is different from sqlite, etc, etc. I've used all the dbs I listed above, but the one I keep coming back to, the one that gets things done most easily and flexibly for me, is MySQL.
DBAs love to put down MySQL the same way programming language aficionados love to bash PHP - and yet they survive and thrive. There are reasons for this - they just work, they just get stuff done. But at the end of the day you should play around with all of it and make up your own mind.
