You could do a couple of things to erase your background noise.
First, turn off any TVs in the background(your first recording was just euggh...).
Second, download Audacity(it's an amazing audio editing program). Whenever you record your game commentary, record the video only with the ingame audio. Record your microphone with something else. Always leave 5 secs without any talking in the beginning of every recording. Then, after you've recorded your commentary, open your mic recording with audacity and use the Noise Removal effect(there are instructions on how to use it). Then your recording will sound somewhat decent. Not the same as a high-end mic, but good enough for basic commentary.