Good reading, thanks for the links. It sounds like my limitation at measuring things will relate to my access (or lack thereof) to an anechoic chamber. Wonder if my alma mater has one available...
An inner room in a house with no windows (maybe a basement room, large bathroom, etc) could get you down there. I'd say the issue is more that you probably couldn't afford the sound meter that will record to the level of quiet you could find for brief periods in the middle of the night.
$100 gets you a hand held sound meter that you can measure down to the quietest spot in your house during a good day.
$1000+ gets you a hand held sound meter that you can measure down to the quietest spot in your house during the quietest night of the year.
$300-$500 worth of parts and software plus a working PC gives you the chance to make a PC setup like what SPCR uses in the chamber but it isn't mobile/hand held and you have to be sure you can turn that working PC into a fanless PC if you don't want it to affect the readings.
Until you go for the options that are well above $300 I don't think you'll need a chamber. You'll just need to be careful when you measure and where you measure and take multiple readings or watch the meter for longer sample periods to reduce the chance of spurious or continuous outside sounds from affecting your readings.
Though if you take a working PC to a chamber at the school it might be good for a single reading. But after that reading your PC configuration may change over time and fans will age and change. So you'll be back to square one at some point (how loud is it after this change?)
And yes what CA_Steve said is absolutely true. Buy parts known to be low noise and you might not care about measuring anything.