IS there much difference between MySQL and PostgreSQL for a beginner like me, using basic select statements and the like, or are the main differences with using more advanced queries?
PostgreSQL supports more advanced queries, it performs better on complicated queries, but is harder to manage.
MySQL is fast, easy to manage, but you can run into it's limitations on advanced queries, stored procedures and the like.
They are sufficiently similar that I'd recommend starting with MySQL but learning PostgreSQL as well.
The reason why I usually suggest PostgreSQL before MySQL is because MySQL is far from the standards (SQL-wise). It does not support the use of window functions (8.4 version), common table expressions (8.4), CHECK constraints, EXCEPT/MINUS operator, even FULL OUTER JOINs... Even though you may have never heard of these words, you'll have to use those concepts at some point.
I strongly suggest you to start with PostgreSQL, then you can learn what "real" SQL is. Then, you can decide if MySQL is sufficient or not.
P.S. I started with MySQL and I regretted it. I now use PostgreSQL and I love it.
While you're just starting out I think you'll appreciate PostgreSQL's pgadminIII GUI tool more than you would those that I've tried for MySQL. This may just be my preference, however.
When you get past the basics you will definitely want to take advantage of PostgreSQL's support of window functions starting in version 8.4
I'd actually recommend PostgreSQL over MySQL for the window functions alone. Note that there are ways to emulate window functions in MySQL.