Personally I've been using Sony Vegas 7 which is pretty powerful, although I really have no idea what the heck I am doing with it. Chances are I'd be just as well off with a lesser program with easier to use functions. However, I'm a dork and like the challenge of figuring out "new" stuff.
If I was in your shoes I would look into picking up a copy of Adobe Premiere Elements. I think you can get it for around $100. It's basically a slimmed-down version of the program that a lot of professionals use for video editing, made specifically for the home consumer.
In regards to your computer its about the same as what I've got at home, which I've found is a little underpowered for efficient video editing. I can edit/chop/splice/hack stuff together alright, but when it comes time to render the final video file forget about it. Half the time I go to bed and let it render overnight because it takes forever. I'd say if you're going to do a decent amount of editing to upgrade. You'll want a dual core processor and at least 2GB of RAM for sure.
Hard drives are cheap so don't worry too much about getting the biggest internal drive you can find. Each standard definition tape captured in full to your hard drive takes up about 13 GB of space, so plan accordingly. Even in my limited amount of fimling this year I chewed through 20 hours of tape, which took up 200+ GB of my 500 GB external drive. But like I said, they're cheap and you can always buy more.
That's all I've got. Take it for what it's worth, I only halfway know what I'm talking about. Kind of like most things in life.
Editing software?
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