Look locally first and if you don't find any that suits what you want then start looking at importing. 15k for a GTR, expect to put in at the very least another $5000 to get the car fixed up. No real advantage to a later model mainly just not being as old as a 1989 model. As for problems, just generally wear and tear on a 18+ year old performance car, also coil packs, AFM's and o2 sensors seem to be pretty common problems. Rebuilt would be the way to go if the work has been done by a workshop that know their way around skylines, and make sure they have all receipts for the work done. I have been insured by both JustCars and Shannon's and both have been around $2000 a year with a $1500 excess (JustCars )and $900 (Shannons).
My car was on the boat to Australia while I was still on my p plates and got the car not long after I had turned 20. I haven't had any problems in nearly 1.5 years of owning the car.