If you want to do high end professional type stuff, then CS3 and Final Cut Pro are the standards. They are also 64 bit compatible as I understand it.
If it is just home movie, or You Tube type stuff, then Windows Movie Maker for free, or Sony Vegas, and a few other sub $100 packages will be fine. For these programs, you can actually get by pretty well with 2gb ram and a Core2Duo.
I use Windows Movie Maker to edit and encode to .avi. I then use Cyber Link Power Producer to burn to DVD. I have yet another free program called Avidemux that I use to convert formats. It does other stuff as well, but is a bit too involved for my taste.
With SP1 coming out soon, 64 bit Vista might be a good option. Just check for drivers an whatever hardware and peripherals you wind up with.