I am hardly the most knowledgable on this subject but I'll chuck in my 2 cents anyway.
With that budget and your age I would go with either an R32 GTST or an R33 GTS25T. A GT-R in that price range wouldn't be in great condition (if you could even find one for 16k), not to mention it would cost more to insure, run and I'm sure general maintenace would also be more expensive.
As for the R34, again in that price range you'd be looking at a sedan and/or a non-turbo which I'm sure you don't want.
Then if you want a decent sound system, body kit and other extras that is going to cost even more money, so factor that in aswell.
If you can find a decent 2nd hand R32 GTST or R33 GTS25T with maybe a bodykit and/or an alright sound system already on it and in your price bracket you will probably be onto a winner.
Although if you could find an R31 with an RB20DET (R31 GTST's I believe they are called) you would be pretty rad in my books.
Just my thoughts though. There are many more members on this board who know Skylines alot better than I so I would be listening to them first.