Greycap
My suggestion as the competition car is the Amuse S2000 R1.
I second that. I have heard so much about what this car can do on the Nordschleife. Supposedly, it can win a 200-pt 24h. I have personally not done too much testing with it, but I'd like to see what kind of times everyone can come up with.
I've come close to 6'45 in the AMG 190 Touring Car and I think I have gone below that in the M3 GTR, but since I have no proof and don't exactly remember, I won't make any claims just yet. I'll run some laps when I get home later.
Other than that, you can try to beat my 24h fastest lap of 7'03.560 in the Altezza Touring Car, stock, R1/R1...although I don't expect that will be too hard. First person under 7'00, perhaps?
Edit: Some times that I just ran:
Merc. AMG 190 Touring Car, stock, R3/R3 - 6'46.794
BMW M3 GTR Race Car, stock, R3/R3 - 6'33.627
Amuse S2000 R1, stock except for R1/R1 - 7'32.952
^^ I haven't had as much track time with this car and it handles very differently from the DTM's I've been driving (more drift-y?). I suspect it can easily post times under 7'30. It would probably be better with R2/R2, but I originally was testing for the Nurb 24h so I put on the endurance tires.