The professional choice for video editing on Windows has historically been Avid, and there used to be a basic free version available (though this seems to have been discontinued). Next choice would be Adobe Premiere, which has improved a lot in recent years.

Neither is cheap. For rough (and I mean rough) editing you might use QuickTime Pro, but you will not be able to add effects or transitions (though you can insert still image files for captions).

I am not aware of any good video editors for Linux - there are free options such as Jahshaka but I have never found them satisfactory. I personally use FinalCut Pro on MacOS.

To get the video to your computer you only need a firewire cable and firewire port. If you don't have a firewire port you can pick a pci firewire card up really cheap. Your assumption is correct, it's quite easy to transfer and isn't much different than copying a file from one folder to another. Only difference is it has to be done real time, 1 hour of footage takes one hour and there is no error checking so your comp has to keep up with the input which is pretty much a moot point with any modern computer even going back a few years.

For some advanced editing without the huge price tag Ulead Video Studio is about the best you'll get. Lots of advanced features and it will go from capture to burn. The higher end editors like Premiere have a lot of functionality but your average user is not going to need such features. Do you need unlimited overlay tracks? You most likely won't use the 3 or 4 Video Studio provides...

Having said that most people that do this a lot have a arsenal of tools. Some tools just work better than others, what you need really depends on what you're doing. Some are free others can cost a fortune.

For free Windows Movie maker is OK but it's really limited and there are many things it simply cannot do. If you get serious about it by the time you start to figure it out you'll learn it's simply not enough.

there is a basic video editor which includes some effects built into vista.

That would be Windows Movie Maker.

Just to add tools are important but having the knowledge to use them correctly is more important.

Start with Windows Moviemaker. It's free and incredibly easy to use. Once you outgrow it, then splash out the cash.