My recording setup got significantly simpler when I started using FRAPS (though bear in mind it can't hook into games that don't use DirectX/OpenGL, maybe one of the two, I can't really remember.) I had to record three different channels when I was using the manual screen-recording method, but now it's down to two - and FRAPS by some black magic has the ability to record from both microphone and speaker output at the same time if you choose to do it, and that would bring it to just one (with no need for a microphone laptop). The only reason I didn't was that I like having the game audio separate from my voice - it allows for editing that's just a little more professional, especially if I can eliminate any involuntary breathing/coughing noises on my part.

I forgot about Google Plus (which we may have to permanently, if they don't fix this horrendous feature and any other games are particularly keyboard-heavy!) - for an unedited play session, yes, that really is all you need.