To begin with answering the latter question - yes, nowadays you can definitely edit video quite reliably using a Windows (XP or Vista) as your platform. It may still hold true that Mac OS is a more stable environment over all, but I find it more important that the hardware of your chosen PC is reasonably up to date.
If you have a fairly new Windows PC with a large enough hard drive, the most natural choice is to get software that works on this system, instead of forking out a few thousand dollars on a brand new Mac just to edit videos on.
So what editing software should I buy?
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Premiere Elements is the younger sibling of Premiere Pro, and the actual editing happens in very much the same way. Elements is more consumer friendly though, which is immediately apparent in the colorful main menus: Organize, Edit, Disc Menus and Share. Under Edit you will find options for getting media from the hard drive or from your camera, as well as icons for accessing effects, fades, titles and more. Everything is very well laid out and accessible.
The effects build on what one is used from seeing in Adobe Photoshop, and work very well indeed. There are also ready made themes to choose from. In version 4 these were quite unimpressive, but have now gotten better and, if you want, you can get even more of these themes by signing up for the (paid) Photoshop Plus service.
A feature I have liked since its introduction is the "Edit to the Beat" feature. Here the program automatically analyzes a music file on the time line in order to automatically put markers on every beat. This makes it a lot easier for the beginner to make a cool music video with cuts that actually happen in time with the music. This is more fun than it sounds, promise!
The newer "SmartSound" feature is an even easier way of automatically adjusting the music to perfectly match the length of your movie or for auto-synchronizing scenes to the beat of your soundtrack.
A couple of reservations
On the whole, I think Adobe Premiere Elements is as good or better than many of the competitors in the same price range. However, there are a couple of reservations that may prove to be real show stoppers for you. Namely:
1. You can't burn Avchd/Blu-ray to ordinary DVD discs.
This may perhaps not be a huge issue for many, but with some other HD video editing softwares you can actually burn the structure of a blu-ray disc onto an ordinary DVD disc, which then can be played in any blu-ray player. A standard DVD will hold about 20 - 40 minutes of high definition material, which may certainly be sufficient for many of the projects you wish to burn to a disc. As recordable DVDs are much cheaper than blank blu-ray discs, you could potentially save a lot of money with this feature.
I am not sure, but one would think that this issue would be possible to solve with a future patch/update of the software? It took a while for the people at adobe to implement AVCHD in the first place as well, but that now works flawlessly.
2. Premiere Elements Require SSE2 support from your processor.
If the processor in your computer does not support this architecture, Premiere Elements won't even install on your computer. In practise, this means that any AMD Athlon processor prior to the Athlon 64, including ALL Socket A-based CPUs, are NOT compatible with Premiere Elements. This is a pity, as I imagine the faster models of these CPUs would be quite able to run the software.
You can find a complete list of compatible CPUs here, and the Premiere Elements is also available for trial download from Adobe's website, so you can test compatibility before making up your mind.
Conclusion
All in all, for most owners of a Windows PC, I am happy to recommend Adobe Premiere Elements as the overall best choice of video editing software. It is affordable, easy to use and allows you to pull of some pretty spectacular stuff - it is almost perfect. If you use Photoshop or other Adobe programs (After Effects is really cool!) it naturally also integrates very well with these.
If one or both of the reservations I mentioned above applies to you, my second choice would probably be Corel VideoStudio Pro X2. That is also an editor that is intuitive to use and that support both older CPUs and burning blu-ray material directly to standard DVDs.