If you want to walk before you run, try Pinnacle Studio 8 or iMovie first before Premiere. Simple intuitive interfaces on both. Both very cheap (iMovie free with all macs, Pinnacle software is about £40 with a firewire card if you don't already have a IEEE1394 (firewire) card/interface on your system).
However Matt, I would imagine with your background you will be used to multitrack editing n a PC/mac so I imagine Dave's advice may be more suitable as Premiere uses multiple tracks similar to music progs...
All that said, in a few years when you're stepping up to lens your first feature go for Final Cut Pro or Avid