For Postgres reading material, I'd suggest the Postgres docs themselves: They are through, and easy to find stuff in. (At least for me. I find the MySQL docs horrible.)

Add to that some general database books if you have never worked with databases before. Sorry, I don't have any recommendations for those.

As for benefits: It scales better to large datasets, it has a fuller selection of database features, and it operates very close to the official spec for SQL. (Where MySQL deviates fairly widely from it on occasion. Which can be nice on occasion, but it means you'd be learning bad habits in those cases.)

If you just want to learn, and are really care about 'small, fast, easy', SQLite might also be worth a look. There isn't a smaller database out there, it's still very fast, and it's definitely the easiest to set up. But it has a very different audience. (Although it follows the SQL spec better than MySQL, and has some features MySQL is missing...)

I've also found either of the above much easier to use and install with Perl than MySQL, but that seems to be a fairly local thing. (Although the DBD::Mysql docs have huge 'if it doesn't work' sections...)