In the primordial past (college, early 1980's) I used a fairly small box (about an 18"~24" cube IIRC) lined inside with absorption to measure near-field performance over most of the frequency range. Bass response was tough without a real anechoic chamber (which I had access to at the time; these days, the local college has a nice one, but I'd have to pay to use it or rope one of my friends on staff to help). The box when sealed had a pretty low noise floor after I wised up and suspended the measurement box within a larger box with thick walls and so forth to better isolate the measurement box from the outside world. And tended to test later at night when the building was quieter.
The bigger problem for me was getting a source that was known good over a wide range of frequency and dynamics. The good measurement mics often outdid the drivers used to send test signals to the mics. I had some piezo and compression drivers that were OK from maybe a few hundred Hz but sub-100 Hz I am not sure I was ever satisfied I knew what was limiting the measurements. My Earthworks was good to 5 Hz and at that time I had no good low-distortion driver flat to 5 Hz around.
But again, not my day job, so I was probably just being ignorant, or stupid, or both...
Or too early to the game. The key to getting good midband and HF measurements is gating the impulse response, which wasn't easy in the early '80s unless you were lucky enough to have Nicolet FFT gear (the NIC system I used then was >$100k). You do need a calibrated reference mike (I based my measurements off a B&K 4133 for most of my reviews, but have a new reference now). Ditto your sound source- it doesn't need to be flat, you can normalize it out. You do need a way of getting the diaphragm position repeatable for substitution, in my case a hanging string and golf ball, which are secured out of the way during measurements. A turntable with the diaphragm centered will allow you to get polar pattern data.
Noise floor measurements require isolation, either something like your box or, if you really want to plumb the depths, the BLANK chamber I use (which has allowed me to measure noise below 5 dB SPL).
Distortion is best done at a moderately low frequency in a nearfield setup. Most cheaper test mikes which otherwise look fine for frequency response fall apart in this test. Some expensive ones do, too. Here's a good expensive one versus a superb expensive one: