Check out the link at the bottom of my sig. There is a guide there specifically for getting Video Game footage.
As for a video editor, they aren't really that cheap. I use Premiere it's costly $500 or so new. Though you can get it bundled with a DV200 for around $250. Everything else is going to cost you $100 or so.
There are a bunch of Trial/Demo versions of video editing programs out there. Premiere is included. You can pick it up @ www.adobe.com
. I would read the guides here first before you attempt to make a video. This will save you some confusion/headaches