Since you know Perl and C (especially Perl), you'll have no trouble picking up PHP. The basic language syntax, operators and features (loops, control structures, etc.) are the same or similar to other languages.
The major difference between PHP and Perl is the object model. In Perl 5, the object stuff evolved out of what was present in the language (especially references), so it's not a true object-based language (which will change in Perl 6).
PHP's object model is very similar to Java's. Note that I said "similar" (before I get flamed by the Java crowd). But if you understand the common concepts of objects (encapsulation, inheritance, etc), you'll be fine. And there's no requirement to use objects (unlike Java, where everything is in classes). But having an understanding of them will help when you want to use add-on modules from other sources (like PEAR).
You should have a good understanding of how HTML/XHTML works, since PHP is tied closely to web use. You can integrate PHP into HTML pages, or visa versa. PHP can generate HTML for you as well, with simple print and echo statements.
And there are MySQL methods built right into the language, so integrating with that is a snap. There's libraries for all major databases, so you'll be able to use what you want.
There are a ton of PHP/MySQL books out there...you might check the user ratings at Amazon for some clues as to which ones are good and which ones suck. I learned on the fly myself, from just sitting and writing code, and referring to the PHP manual on their website and using one reference book (Core PHP Programming - out of print), but the PHP web site is a much more accurate source for what's currently in the language.
One other thing I would recommend. Get comfortable with the environment, including Apache. I know you probably come from a Windows environment (the VB reference was a clue ;-] ), but you might want to set up a system with a current Linux distro, then install the packages for Apache server, PHP and MySQL. You can run the entire environment from a laptop, and you can dual boot back into Windows. I say this only because the setup of all the tools is infinitely simpler with most current Linux distributions (not out of my hatred for Windows...).
Good hacking.
