If you're looking just to complete the race, use the X1.
If you're actually looking to RACE, then try any of the Nissan GT-R, Honda NSX, or Toyota Supra Racing cars. My (aside from race tuned) stock Corvette C6 RM was fun. Theres PLENTY of decent cars to try, though I don't drive on the Nordschleife often, and can't give you a specific answer.
Yes, driving style will help conserve tires. More cautious braking and steering, gentle throttle upon exit of a corner are good ways to start. You'll save you're tires a bit more by not going 100%. Thats the point of endurance racing; seeing how well you and the car can hold up over a long period of time, and making the most efficient laps as possible.