i went through that a few months ago, with my NA 33, i got quoted by just cars for $3000 for full comp, so i went with 3rd party+fire+thief for $650.
by the way, it doesnt really matter anymore whether u insure it under ur name or ur parents, since ur on ur P's and driving a skyline, they will still charge u the same, so might aswell put it under ur name and get a better rating for when u get off ur P's.