From personal experience I can safely say STAY AWAY FROM PCs when it comes to video editing. I'm a PC guy who recently got his first Mac. The PC is faster, and rocks for games, but video editing is hands down down strictly on my Mac with Final Cut.
Honestly, the 32 MB of VRAM in the eMac would kill any possibility of using it as a video editing machine. If you're really stuck with that budget, I'd say get a single proc 1.6 GHz G5 and drop two gigs of aftermarket (not Apple) RAM into it. That will just about max out your budget.
You didn't mention how intensive your video work would be. If you're just going to tinker and make home movies or school projects, then any G4 Mac with 768 MB of RAM would be fine. But if you need a lot of effects and transitions, you'll want something a little better. Realistically you'd want a dual processor G5 with a couple gigs of RAM, but that of course goes way over your budget.
Also keep in mind, Steve Jobs is expected to announce a new lineup of G5s on June 28th, and at that point, it's rumored that all G5 systems will be dual processor, while the baseline system keeps the same pricepoint. This, would be ideal for your situation.