At one time it was common to use general purpose omnis for measurement work, but these days microphones designed specifically for measurement abound.
Most practitioners will eventually end up with two mics – one for general field work and another for that occasional precision application.
I’d look at the Audix TR-40A (~$200) at the low end and the DPA 4007 ($1700) at the high end.
This will give you a feel for the range of choices.
There are many units to pick from between these two extremes in the marketplace, including Earthworks, Josephson, TestMic and Gold-line.
Some Frills
The previous items form the bedrock of any measurement rig. There are some other items to consider that will add speed, convenience and accuracy to the basic kit.
Calibrator: Many acoustic measurements do not require absolute calibration. It is enough to know the deviation from some reference response. SPL, STI and noise measurements require absolute calibration. The easiest way to accomplish this is to use a calibrator for your microphone.
Calibrators are fitted to the mic and produce a reference level (typically 94 dB or 114 dB ref. 20uPa) for the measurement system. A low cost calibrator may not be traceable regarding certification.
If this is an issue, the price goes way up. Don’t sweat it. If you need one of these you will know it.
Wireless: I have never met anyone who has invested in a wireless system for measurement that has regretted it.