Up to 2006 the GT-R was a Skyline, sharing the same car body but In 2007 the GT-R became it's own separate car line no longer based on the Skyline body. The GT-R is a higher end and faster model than the Skyline, all are 4wd with twin turbos, it is a true supercar now. The Skylines were imported in to the USA as the Infiniti G35 and now as the G37.
You you could correctly say you still want The Skyline GT-R, R34 was made from 1999 to 2002, in 1998 it was called the GT-T. He is only correct that the newer cars are indeed different since 2007 but as for the older R34 you are yourself correct.
I fear you have allowed too many hours of car video games have made the name Skyline way more legendary than it deserves. In the real world you will not find a JDM R34 import then modified to be US street legal, not cheaply, nor would any teenager be able to afford the car insurance unless your parents are very wealthy.
Paul Walkers movie Skyline was a $20,000 car which he spent another $200,000 on to make run as fast it did in the movies. That car was for sale at the time of his untimely death for $165,000, now they are asking $1.5 million USD.