Hey mate. I'm looking for an r33 s2 myself. Sorry to burst your bubble but...r33 gtst's only go that cheap if they do have engine problems, over 150,000 k's and have no rego or rwc.
The cheapest I've seen one for is $8k. It's actually not that far down the forum list you should have a look at it. Not ire if it will meet all your criteria but it's certainly worth a look.
Like I said though, I would have a budget of more like $10-11k. That way you WILL meet all your criteria. That's my budget anyways and I'm looking for the same as you
Hopefully that helps mate. Good luck.