The best way to do something like this is with Flash Catalyst's "Pages/States" feature. Each major "screen" or "page" of your site would be one state. Catalyst then lets you author rich, animated transitions between the states and share common elements (headers, search field, etc.) across multiple states.
Most of your SWF size will come from image assets embedded within the SWF. There are a few ways you can keep SWF size minimized:
I hope that helps!