I wanted to offer my own advice on video game capture, as there are other options out there, and I wanted to give some advice on capturing retro game systems.
HDMI: I've never used one, but I assume the device Daan is talking about is
this.
Component: Can be used for 480i, 480p, 720p or 1080i, but not 1080p. Wii U, Wii, and GameCube (good luck getting a component cable for the last one) all support this. The box I use is a Hauppauge device.
Video/S-Video: For older consoles, this is generally what you'll be using. Capture cards for these standard-def connections are fairly cheap, but you'll have to worry about deinterlacing the video. Here's a video I made a while back that explains the process:
https://www.youtube.com/watch?v=IrmeL3A_B6oUsing the techniques described in the video, you can achieve results that rival emulator-captured video.
RF: Some very old consoles only supported hooking up to your TV's antenna/coax jack and tuning to channel 3 or 4. I've never done this one, but you should be able to get it to work with any capture device with a TV tuner.
As far as recording commentary, since neither of the devices I have support a second audio stream, I use a digital personal voice recorder with a headset microphone, then sync the audio by matching up my voice to what's happening on the screen, then move the audio back a few frames (you wouldn't want a reaction to come before it actually happens on screen).