Yeah, I'm pretty adept at this stuff. Been capturing footage for some years now.
First things first, I have a Hauppauge 1212 HD-PVR for capturing footage from newer systems.
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Many people might tell you that you'd be better off getting a capture device that supports actual HDMI hookups, while this one only supports component cables. But the benefit here is that it's more versatile. Not only do newer systems (PS3, 360, Wii; not sure on the newest ones) support component hookups, but the PS2 and original Xbox do as well (the Gamecube does too, but it seems kind of hard to even find a reasonably-priced GC component cable).
Now, you'll also see that there are composite and s-video hookups on the front of it; ignore those. I've tried hooking up my older systems through there, and the signals craps out every time, making recording impossible.
For older systems, I still use my old Pinnacle capture device that I got years ago (which comes together in a set with some really great editing software in the Studio MovieBox Ultimate Collection .
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This one only supports composite AV and s-video hookups, and it's prefect for systems like the Genesis, SNES, or any other old ones. It'll also works with old camcorders or VCRs, so those videos you want to convert would work with this.
And I still, to this day, use the same editing program that comes with it, even though it's technically outdated. Great program, lots of good effects, and it's easy as hell to use.
One of the biggest headaches I've experienced with all this stuff is in getting the best quality possible out of them. Something to keep in mind is that when using these capture devices, the recorded video will only be as big as the console outputs; you can't choose how big the video will be. Older systems actually put out a pretty small resolution, but it gets stretched to fit tvs and you can't tell. Once you see it on a computer screen, however, the lack of quality becomes even more apparent. Stretching it out will generally make it look blurry and ugly.
The best way to get around this (and this just applies to the older systems) is to record in s-video, for one thing, since it offers a much crisper picture quality than the usual composite AV cables do.
The SNES is interesting, because it uses the exact same hookup cables that the Gamecube does, so in that case it's easy to find an s-video cable for it.
Something like the Genesis, however, is a little more irritating, because the system was never equipped for s-video. There are folks out there, though, that can do mods to remedy this. I bought a modded s-video capable Genesis on ebay a couple years back, and it works brilliantly. Even better, the modder included a region switch, so it also works with Japanese games as well.
Anyway, once you have s-video hookups, it's good to record your videos in mpeg2 format. Mpeg2 retains a really high level of picture quality, so even if you stretch the video out, the pixels sort of... retain their individuality, I guess, instead of blurring, so the picture remains crisp and pretty.
As an odd side-note (and something I've only gotten around to recently), if you want the best quality out of PS2 game, in particular, it's best to get an old fat PS3 (60gb or 80gb) which supports PS2 backwards compatibility (you'll know if it's bc if it has four USB ports; newer ones, and older non-bc ones, only have two). The old PS3s actually upscale PS2 games into HD sizes, meaning your resulting video will be much bigger than if you were to record through a PS2.
Likewise, PS1 games are compatible with all PS3s, and get upscaled in the same way.
So really, if you want to record any Sony games, from the PS1 up through the PS3, you just need a good backwards compatible PS3. Makes things easy (though those old systems are prone to eventually dying, so you have to be careful).
I'm theorizing at the moment that the 360 might work the same way... I haven't been able to try out the backwards compatibility with original Xbox games, because I have the most barebones 360 possible, and need an external hard drive in order to try it. One day I'll get to it. Hopefully it'll shoot the games into HD the way the PS3 can, so then I'll be able to record beauties like Otogi, Crimson Sea, or Jet Set Radio Future in awesome quality. One of these days...
Let's see... I'm not sure what else to add. If you have any questions, just post it here. I've run into so many roadblocks and found so many solutions to them that I'll likely have an answer.
Video capture can be kind of pricey, but it's satisfying when you start getting the results you want.