PHP is a language. Since you seem to want to use a database you'll need to learn PHP but the fundamentals of web design are going to be learned in HTML.
I highly recommend familiarizing yourself with HTML to the point where you could design a simple page in Notepad -before- even starting to use Dreamweaver or you run the risk of completely skipping over learning the basics of web coding. Dreamweaver is nice because you can view the design in WYSIWYG (what you see is what you get) mode, code, and a split screen between both. You can learn a lot from clicking on an object, such as a table, in the WYSIWYG view and then hitting the code tab and seeing its exact code (clicking the object will highlight its code in the code view).
MySQL can be used freely where as Access is a Microsoft product. If a host offers a database solution 9 times out of 10 it will be MySQL with phpMyAdmin as a web interface. That is the de facto standard, although there are other solutions available (which may incur an additional cost).
Most webservers run on *NIX type system, eg. Linux, FreeBSD, or other Unix variants. If you want to use ASP (kind of like Microsoft's implementation of PHP) you'll need to be on a server running Windows. This kind of hosting can cost more because it's more rare to find a host running in a Windows environment. I wouldn't worry about about it and only mention it as something to be aware off. You said you want to use PHP so it should run on pretty much anything.
If you're going to be creating your own media graphics most professional work is done in Adobe's Illustrator, Photoshop, and Flash. There are free alternatives to Illustrator and Photoshop but Flash seems to be pretty much proprietary. You won't need to learn Flash for a while though.
As you start developing your site you'll come across other code like JavaScript (not to be confused with Java which is entirely different), DHTML, CSS, and a ton of other stuff that should make sense after a quick read through - just look it up on www.wikipedia.org for a quick run down on its specific uses.