Although more difficult and expensive, it'd be better for Pakistan to design and produce a suitable frigate on its own. I'm not saying this because I want the PN to have its own program for the sake of it, but because it'll give the PN most flexibility and room to decide on the weapon systems and electronics to use on their ships.
Going Chinese may result in having to depend on China 100%, if not for cost reasons then for possible political and technical concerns on the part of non-Chinese suppliers.
A good solution would be to take the JF-17-route in frigates. Work on a general design with China and master the development process within Pakistan so that it'd be Pakistan who will be integrating the subsystems into the design. With that secured, the PN can go around secure systems from Turkey, France, UK and wherever else.
This my proposal:
1. Work with China on a 3500-4000 ton multi-mission frigate design that is capable of housing VLS and other current (as well as future) systems. Make sure the design is stealthy, perhaps to the level of Singapore's Formidable Class or DCNS FM400. Acquire enough expertise to produce the frigate indigenously and undertake most if not all future development associated with it.
2. Work with MBDA on a medium-range SAM solution, perhaps Sylver with Aster 15, maybe Exocet MM40 Block III, MILAS etc.
3. An alternate would be to work with South Africa and others to work in more homegrown SAM, AShM and ASW solutions.
4. Over the long-term make it a plan to form the mainstay the fleet with these frigates, e.g. 8-12.