First let me say: I'm new myself.
Second, that's a beginners method there, in fact I learned from him too (the first video (series) you linked. And, I'm currently teaching that to a few friends.
When I decided to move on and go a little faster, like a week ago, I was advised by people here to learn F2L, which, at first will slow you down a little but speeds up as you get better. I'm starting to see this now. At first it doubled my times, but the past few days I've got a good amount below my beginner method averages, and records..
So, I definately can see where this is going.
I was advised to start here, there are two video's, and I'm glad I did so I'll recommend them to you.
http://www.youtube.com/watch?v=k-xbcAMfWwM&feature=channel_page
When you've learned it and are okay with it you can look in his channel for some advanced tips for F2L, which I've very recently started to try to employ. He also has some other helpful videos, like how to hold the cube for finger flicks (well, finger tricks everyone else says) and stuff, which I liked.
Good luck! And welcome..