MIL-S-8879 section 4.4.3 basically states any inspection method described in FED-STD-H28/20 or ANSI/ASME B1.3M is acceptable provided the inspection method assures conformance to the requirements listed in MIL-S-8879. The best choice of inspection technique depends on the particular application. Johnson gaging fixtures are a bit pricey, but they provide actual dimensional/tolerance data. If you are conducting a first article inspection you may be required to record actual measurements, which Go/No-Go gauges don't allow.
Go/No-Go ring and plug gages are not as expensive, but they only provide a pass/fail result. If the threads are being produced by different outside vendors the ring and plug gages are easy to transport and are far less likely to be damaged. Ring and plug gages also make it easy to perform a quick inspection of the thread while the part is still set up on the machine.
I've attached the relevant section of MIL-S-8879 for your reference.