I brought my 1993 R33 gtst over from Sydney about 4 years ago
The ID check at regency is pretty painless they just had a quick look at the car, barely looked at the engine took under 30 minutes. But I did remove the aftermarket BOV and air filter before I took it there. The car had also been lowered and had illegally dark window tinting.
The guy tested the tinting and said it was too dark but he only recommended I remove it, I didn't remove it and still have it now 4 years later with no problems, they didnt mention anything about the height of the car. My mates said I was ok because the car is white and I was wearing a suit
Once the ID check is completed you go to the motor registration office where you get new licence plates and pay for your new registration plus stamp duty plus a fee for re registering the car. Because your car was most likely expensive you should check the stamp duty rate here:
http://www.revenuesa.sa.gov.au/index.html?http://www.revenuesa.sa.gov.au/stamps/stampd.html
It cost me at least $500 to register and transfer my car.
I calculated the stamp duty for a $40,000 GTR it is $1,540 plus the transfer and registration fees so I wouldn't go there with under $2,000.
As for insurance I use just cars. They are one of the few people that will insure an import without requiring a lock up garage, just MAKE SURE YOU GET AN IMMOBILISER AND ALARM!!!!
I haven't claimed though just cars so I can't say what that is like.
Hope this was of some help