Vincent Hancock's 'trick' is to hardly move his gun at all, notice how he keeps it within a few degrees of the breaking points of both the clays. He 'stacks' the HH and LH clays, virtually shooting them in the same place. For us mere mortals that's great to aspire to, but incredibly hard to achieve. But if you shoot 120K+ carts a year, you could get there eventually. The point is that he is so experienced that he can "follow" the clays trajectory while still "just pointing" the gun in the right spot to break it. Most if not all of the shooters I know need to at least follow the clay for a part of the trajectory with their gun, and just stabbing it at a desired spot doesn't get them very far.
Most of that movement should come from the waist, but adjusting for height and trajectory of the clay is mostly in the steering hand. Or at least that's how I shoot - mind you I'm not even fractionally near VH's skill level. By comparison I move way way more and need to swing the gun from clay to clay. Surprisingly I do hit a few, but it's inspiring to see how much less effort better shooters need to exert.
As to the gun question: If you shoot skeet ' just for fun', shoot anything that you have or want. If you want an actual skeet gun I am assuming that you will also want to shoot Olympic Skeet (because the rest is less is skeet for... <edit> I mean less challenging). For skeet I wouldn't recommend anything over 30" (especially not with extended chokes), preferably with light barrels and balanced a bit to the rear. The longer the gun the harder it will be move it quickly. Some shooters prefer 28 inch to 26 even, but with modern barrels its not a requirement. Open chokes are best, SK and SK being preferable for OS.
