For putting that much power down, you really cannot beat AWD. I don't really know what various cars are capable of through tuning, though.
You've already mentioned the GT-R and 911 Turbo. They're probably the best fit for what you're looking for, with the Nissan obviously less expensive than the Porsche.
An Audi R8 might also be a possibility, though they are naturally aspirated and so will be more expensive to get a lot of power out of. The Audi TT RS is very quick 0-60 even stock, and can be tuned for more, though 800 crank horsepower is probably a stretch.
If you're willing to give up low-speed traction, then you have quite a few rear-drive options.
The C7 Z06 performs incredibly for what it costs. But a Corvette isn't really a straight-line car, and even with the stock horsepower I hear handling can be tricky.
Both the Mustang and the Camaro can be tuned for 800 horsepower at minimal cost. I don't know if either is your thing, though.
Finally, there is of course the Dodge Challenger Hellcat. But it's a far different car than those you mentioned.