What you need to run flash depends what you are using it for.
IF for animation, purchase Flash MX 2004 and get started.
for development,(I suspect You are one :-)
purchase Flash Mx2004 Professional.
If you want to create 3 tier applications, u need a web server like apache/ Win IIS installed and configured to run ASP or PHP or a server side Lang of your choice.
Furthermore, You also have a choice of using Flash Remoting for client-server interaction.that of cource requires you to install the remoting environment.
As you mentioned that you are a beginner, it would be wise to start learning with the right perspective.
Hope this helps :-)