Take every Photoshop tutorial you can get your hands on. Text effects, general effects...these will all acclimate you to the tools and will aid future projects when you're trying to visualize the steps it will take to produce a certain effect.
Do not think that Illustrator and Photoshop are the same - in fact, they are far from it. While many hotkeys are the same, the way you manipulate objects that you create is entirely different. Biggest and best pointer: DO NOT FEAR THE PEN TOOL! It is NOT as hard as people make it out to be. It takes some finagling to get used to but it is very powerful and can produce stunning results.
Dreamweaver can be learned in one of two ways: the code perspective, or the design perspective. That is, you can create a webpage in Dreamweaver solely in the design tab and inserting tables, editing their properties with the properties editor, and adding content. That's fine and dandy. OR you can do a combination of design and code work. Create a map in the design tab and then fine-tune in the code. This will take a good knowledge of HTML, but it's pretty straightforward once you get past learning the syntax and basic keywords. A good way to learn web-coding if you don't already know it is to go to your favorite website, then, depending on your browser, view the source code. In Safari, go to View -> View Source. Look at the code side-by-side with the site and see how elements are graphically laid out with the code.
As far as Flash goes, I can't really say much - I don't really know it all that well. I need to learn ActionScripting...But don't think that you absolutely NEED Flash to create a kick-butt website - CSS and Javascript are your friend. But that's a whole 'nother chapter.
As far as the order in which you should approach learning the software bundle, I would DEFINITELY say Photoshop first. Master it. Once you do that, turning a web template that you create in Photoshop into a working site is as simple as slicing and saving (you'll learn this on Lynda...I've seen those tutorials before and they're GREAT for beginners such as yourself). There are plenty of established web design firms that produce stunning content with just Photoshop, Dreamweaver, and CSS/Javascript - as I said, don't rush into Flash. That's the cheese on the burger. You'll be just fine without it, but it is nice to have it once in a while. As far as Illustrator goes, it will be great for creating logos and other branding materials, but in my experience (most recent site
http://www.cathedral-irish.org), I find that I RARELY use Illustrator when creating a web design.
HOWEVER, since you did say you're interested in becoming a freelance graphic designer, that's another can o' worms. Illustrator should be the FIRST thing that you learn. Corporate branding simply cannot be done in a non-vector format. I can say from experience that 99.9% of the time the client will want their logo/letterhead/business card/poster/packaging/vehicle wrap in VECTOR format. Vector should scream Illustrator. If this is the path you're most interested in pursuing, exit out of Photoshop and learn Illustrator. Don't get me wrong, you'll need both, but Illustrator is much more important.
So it's a decision on your part. Web or graphics? It doesn't have to be a decision at all - I do both and have been successful in both areas for many years (just turned 20). But when it comes to the question as to what to learn first, ask yourself that question. Don't do little-by-little. Immerse yourself and master it, and you'll find the others are more easily learned as well.