There are LS6 GM's out there that will run 11's all day long. Although easy to do, they are fairly expensive to get to that level of performance.
Here's the best recipe I can give you for that level of performance:
Buy an 03/04 Cobra. Add a CAI, catback, pulley, and tune. That should cost you somewhere in the neighborhood of a grand and will easily get you in the 11's. You may have to add a set of rear tires to do that though...you will fry the stockers.
If that's not enough for you, take the blower off and have it ported. To do that and the throttle body should be somewhere around $750. Again, you will need to have the car tuned. That will get you somewhere around mid to low 11's.
Still not satisfied? Bolt on a Whipple or Kenne Bell. That will probably require fuel and MAF sensor upgrades too. Properly prepared, that could get you into the 10's. Those blowers can be found for around $3000 used, about $800 more new. This should easily get you over the 600 hp mark.
With all these mods done, the car is still 100% streetable and you haven't had to touch the inside of the motor. The stock motor can handle that kind of hp easily if you don't lose your mind with your new found power. But at 600 hp, if you go insane and run the thing to 170 mph for a while, you can have issues. Normal driving and the occasional drag race shouldn't be a problem. If you are serious about drag racing the car, I would pull the IRS and go to a straight axle. They are a bolt in swap and won't cost a lot to do if you sell your IRS to one of the Mustang guys who want to go twistie racing. There are quite a few that do...
Good luck!!
P.S. By the way...an 11 second car is very common these days on the street. In fact, there are several 10 second cars running around here. A few Cobras...Supras...Vipers...Z06's. The reason I say this is because you stated you want to build a "very fast" car. My God...you would think that a 10 or 11 second car is scary fast...and I guess it really is...but it seems EVERYONE is doing that now!!!
