Personally I'd just build a custom desk and get a watercooling setup and put the base unit into a hidden compartment in the desk itself. That way no mentally long cables, risk of dust killing it or awful fire hazard.
This is what I'd do too, either a custom desk or some sort of side unit to store the case in. Then line it with sound proofing material?
Not sure if this is suitable, but you get the idea..
https://www.noisestopsystems.co.uk/soundproofing-walls-6/barrier-shield-4.html
http://www.keepitquiet.co.uk/help.html