I tend to use the 'poke a hole in the middle' method, but my bagels are usually about 3 ounces of dough, the ones you'll get at a bagel shop will generally be somewhere between 4.5 and 6 ounces each, so the 'wrap around the hand' method works well, especially if your dough is as soft and developed as the ones in those videos. (Mine seldom is.)
I find boiling them for about 45 seconds then flipping them over and boiling them for another 45 seconds works best, but as the second video notes, the timing of each step varies from day to day, some days the dough has to rise longer, other days it needs to boil a little longer.
There was an interesting discussion in the Bread Bakers Guild forums a while back about whether or not bagels should be boiled in lye (or some other alkaline solution.) This is one of those areas where bakers get pretty passionate, the majority of the Guild members were very opposed to using lye, though I know of some NYC shops that use it. (Pretzels are another matter, using lye or baking soda when boiling them is pretty much universally approved.)
I did some testing, and when I used an alkaline solution, baking soda, the surface of the bagels got darker. I don't think it affected texture much.
What the boiling does is to gelatinize the starch on the surface, which changes the surface texture to add some shininess and a bit of a snap when you bite in. I think it may also help hold the toppings on.
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