Guys... read his post. He wants to be able to break 10 hand thrown clays at a time.
Try that with a Browning Citori, Perazzi, or Krieghoff.
Shooting the box of clays doesn't count.
Fishy, there's not a particular choke that will make it easy to break a dozen clays in the air. I imagine the trick shooters use more open chokes because they're not shooting longer distances. Cylinder bore, skeet, maybe Improved Cylinder.
But I'm not a trick shooter so I can't say for sure... that's just my best guess. They may be so accurate they use modified chokes.
But that's really the last/least of your concerns at this point. With any good semi-auto shotgun (and you are going to want a semi auto for fast work), you can practice a good long while, years maybe, before you get good enough to need more than 5 shots at a time. If/when you do, buy a nordic components or choate magazine tube extension (that's what you're thinking of when you say you want a "type of choke or something that allows some of the clay shooters to load up to 12 shotshells in their gun") as long as you like. I doubt you'll ever get good enough to need more than 8 or 9 shots in the gun, but you never know.
You might just be the next Tom Knapp or Patrick Flannigan.
Generally speaking the 'inertia' driven guns like the Benelli M1/M2 are most favored by "fast" shooters, from what I can tell. But Flannigan's Winchester SX3 is gas operated I believe and is dang fast also.
http://www.youtube.com/watch?v=Dsku5nScBf8
I suspect the majority of respondents to your post are weary of yet another "what's the best shotgun for ______" thread and are trying to be helpful to an obviously uninformed and inexperienced poster.
Good luck, but the bottom line IMO is practice. You might actually find a standard, cheap, 5-shot Remington 870 would work for a long time before you got good enough to need an auto with a mag tube extension.