I researched this when building my own computer for HD video editing about a year ago - I don't remember all of my sources, but there's a hardware guide on the Adobe Primiere Hardware Forum (very helpful place) that was a big help. That guide is several years old, so the specific hardware recommended is out of date, but the principles are still there.
Basically, most gaming PCs are going to have a more powerful graphics card than you need and less RAM than you'll want (and possibly inadequate hard drives). It's better to build yourself, but if you're going to buy an off-the-shelf model, a gaming PC will probably serve you better than one that's not (since most of the manufacturers' high-end stuff is geared toward gamers). There are companies that build PCs specifically for video editing, but they are VERY expensive, especially compared to what you can do yourself. I built mine for around $1000, which is what I would've paid for the Dells and HPs I was looking at, but I was able to get exactly what I wanted.
I don't know about audio, but for video, I'd recommend:
- The fastest processor that fits your budget (use benchmark scores, not clock speeds, to compare)
- Fast hard drives. An ideal setup from what I've read (and based on Premiere benchmarks) is to have a small SSD for your boot drive and a RAID array for the actual editing. Those are fairly expensive, but at minimum, you should have 2 hard drives, one to boot and one to work in (and do NOT get 5400 RPM models).
- A mid-level graphics card. I've got a GeForce GTX 550 Ti and it handles my 1080p/60fps video just fine.
- RAM will depend on what software you're using (as will all of these, but RAM more so). For Premiere CS5+, for instance, you probably want at least 12 GB; I use Lightworks, which is still a 32 bit program as of this writing and therefore can't use more than 4 GB.