The Lewitt is not only low noise, but about among the most sensitive. Those are the two things you most need.
The free software is pretty easy to learn. You might want to read up on FFTs if that is not something you are familiar with. High count FFTs let you look well below the normal noise floor. It is something REW and Multitone let you do. The people who wrote both are members here.
As for calibration an advantage of the Umik 1 is it is self calibrated in REW. As they are less than $100, I might suggest getting one of those and see how far you can get in your testing with it. Then if you later go with a better microphone this one can be used to calibrate the other microphones for SPL. You also might want to get it from Cross Spectrum labs as they calibrate them more carefully. While not the most sensitive or lowest noise the Umik 1 is good enough if the noise is loud enough to be heard you'll likely pick it up. It does have some noise spikes in its noise profile that might be an issue, but still pretty cheap to take a first shot at it without spending too much.