It'd be quite a process getting a fighter capability up and running again in the RNZAF. It's not simply a matter of choosing a plane and paying for it. You need someone to fly it for starters... I don't doubt that there's an ex-Skyhawk pilot or 2 running around the RNZAF who could convert back to fast jets, but they'd need to do a conversion course of some sort.
I think the acquisition of a training aircraft sup as the PC-9 or Super Tucano would be the first step. A lead-in fighter such as the Hawk, of T-45 Goshawk, L-59, Macchi or similar would be the next step, followed "eventually" by a front line fighter.
A plan could be an initial purchase of second hand PC-9's and Hawk's to begin training NZ pilots on their own aircraft. (Conversion courses could then be conducted with the RAAF). Once the initial courses were done, the serious "shopping" could be conducted.
SAAB JAS 39C/D Gripens could be an option. Hungary and the Czech Republic have leased them, so NZ might be able too as well. (They use an F/A-18 Engine too I think GF, the GE F404...) This would provide the benefit of relatively limited initial acquisition cost for a genuine 4th Gen fighter, with high level A2A, air to ground, maritime strike and tactical recce capabilities.
Second-hand F-16's would also be likely, given that they are widely available and fairly cheap, (compared to other available aircraft), these could be sourced from the US, or the Netherlands, Belgium, etc. They could probably only be leased from the US though and would require significant "non-recurring" investment if a maritime strike capability (ie: Harpoon, SLAM-ER) were to be included.
Another option could be F/A-18E/F Super Hornets. They would probably be at the pointy end of what NZ could afford, but would provide excellent capabilities in almost every aspect of air combat, including providing organic tanking and long range strike/maritime strike capabilities. They could also quite possibly be leased from Boeing (a lease was proposed to the RAAF by Boeing as an F-111 "Gap filler"), with ownership transferring to the RNZAF at the end of the lease. They'd also completely obviate the need to spend so much on a strike capability for the P-3K Orions.
I think a fleet of 28-32 fighters of whatever sort, would be sufficient for NZ to acquire 2 operational squadrons, plus an Operational Conversion Unit and attrition aircraft.
It'll be interesting to see if any of this occurs however...