Perfecting the Jab, Cross and Jab, Jab, Cross any suggestions?

Yes, I know what I just said seems like a Boxing 101 for a novice beginner. However, I'm not so proud and so egotistical as to not ask this question. I don't spar or go to the gym anymore, because of work and other issues, but I certainly don't want to get rusty, so I do hit the heavybag often. So here is my question.

When I was sparring and in the gym, I threw a different (perhaps different style) of the Jab-Cross. However when I threw it, it was easy for my opponent to counter with a Cross. No, my defense wasn't down, but the time increment that it took to throw my Jab and then the Cross, left me open. Here is an example of how I typically threw it:

http://www.youtube.com/watch?v=_ZzbzEDVC_A
Note that this guy somewhat angled his head offline to the right when he threw the Jab (and he twisted his hip), and returned to throw the Cross. It was good that he was using head movement, but he could have been open between the Jab and Cross because of the extra time the Jab took to land with the extra rotation.

Here is the Jab, Cross that I think would be most effective, but I want your input on which of these work the best or which ones you think works the best. Note on this one, the Jab is not thrown with the additional twist of the hip, it is thrown straight without head movement. The cross is thrown correctly.

http://www.youtube.com/watch?v=0DRbFla_8cc

Which one is most efficient and probably will land without a possible counter? After answering this, I have one last question. This concerns the Jab, Jab, Cross. Do you throw the first two Jabs hard moving in (like a push Jab) or do you throw two fast Jabs and unload on the Cross? Thanks a lot, for whoever answers :)

did you not receive instruction when you went to the gym? That first 1-2 is kinda shit if you ask me.

yeah the first vid IMO isn't showing you the proper technique, you should learn from your gym, for example, i was taught not to move forward on the cross, and keep all the weight on your back foot. not sure if that's universal, but it makes sense because you'd be easy to counter if you did that.

in the second vid he doesn't turn you toteach the hook over. i hate that.

if you want to learn boxing, go to a gym. period.