[STCrowley]

I like the second, because it is how I'd (American) talk. I say 'I'm about to' when I'm talking about the next thing I'm going to do.

'On the verge of' is normally a bit negative for me. I use it when I'm getting close to doing something I don't want to do: "I'm on the verge of losing my temper" or "I was on the verge of telling him just what an idiot he was." It has more the feeling of being 'pushed' into something by your surroundings.

I hope that has helped some!
Any more questions, just let me know,
-Toby