I would prefer a 3rd frigate definitely and soon with a 4th to follow. If the NZG will only spring for 3 frigates then, stand up the ACF afterwards. Tod makes very good points about the paucity of RNZN frigates and a 3rd one has to take priority, although I believe that it would be possible to do both within the $20 billion CAPEX. However the crunch point is the operational funding being available to pay for the day to day utilisation, which would mean that the Vote: Defence would have to be, most likely doubled. Unfortunately I don't think there is the political will to do so.
Is terms of costings for an ACF, the hurdle I would be most concerned with would be the operational and sustainment costs. This is of course assuming that the full NZD$20 bil. CAPEX funding remains available to the NZDF to purchase new and/or replacement kit, as well as conduct major upgrades to existing kit when needed and appropriate.
Depending on just what aircraft would be selected for an ACF and in what quantities, funding could potentially be stretched to cover the acquisition. What I would really hate to see would be for contracts to be signed purchasing something like 24 F/A-18F Superhornets plus an initial stock of munitions, training sims, etc. Then, following another change in gov't have the new incoming gov't cancel the purchase or if deliveries have already commenced, immediately move to mothball the aircraft, all due to ideological issues regarding the RNZAF having an ACF.
Also when considering an ACF, one should contemplate who the ACF would be operating against, where they would be operating, as well as who they would be supporting and/or operating alongside. I would consider the answers to the above questions very important when considering what combat aircraft to select, as well as in what numbers. If the aircraft are largely intended to provide a self-defence capability in or near NZ, then a fairly basic combat aircraft would be needed for fighter duties to intercept civilian aircraft as well as provide CAS training and some maritime strike.
OTOH if the major role for the ACF would be maritime strike, then honestly I would prefer to skip an ACF and leave more coin available to purchase P-8A Poseidons and a stock of suitable munitions.
Also worth mentioning is that if likely future ACF deployment scenarios involve ACF deployments overseas to potentially hostile areas like a FPDA combat deployment, or if things go bad around Korea, the ECS or SCS, or even to provide air cover for Australia... Then it would be worth planning for such aircraft to be able to be deployed and then operate far from their 'normal' facilities in NZ. That might also mean investing in some additional support gear, as well as transports to provide an 'air bridge' between NZ and whatever the deployment area would be.
It gets to be a complex problem because
nn quantity is required to provide a given level of capability and there are associated costs with that. At the same time, having
nn of something require a given amount of support particularly if deployed away from the 'home' bases and associated infrastructure and support functions, and having the assets to provide that sort of support away from the bases triggers additional costs and support requirements, and so on...