Putting is just like a Normal Swing

[railsroad]

I'm still trying to decipher the teachings from TGM.

I understand that the putting stroke should be just like a full swing except with no body motion.

So does that mean that the putter should be brought straight back along the Target lie, or should it travel in a slight arc on the Plane Line as in a normal swing?

I'm a swinger, but it seems that putting is more a hitting motion.
So I'm trying to use my left hand for alignment and my right hand for thrust.
Is this correct?

This would have the side benefit of turning putting into another club face alignment exercise, which sound like a great idea to me.

It also seems that I should switch my putter back to a more normal golf grip, I've currently got a Enlarged Putter grip.

Sorry for the mass of questions, but there's a lot of details to sort out.

thanks
Bryan
p.s. There seems to be a myriad of different putting methods out there, but I like the idea of the One Swing.