Oh, wonderful, now you have my head in overdrive on two things.
Size. That's easy, standard kitchen cupboard is 60cm wide so if you think something that wouldn't be out of place in a kitchen then there's your answer. Depending on layouts, you might even be able to splice into any extraction above the cooker.
Sound. Now that's where the fun starts. Straight away I think insulation panels since they can be painted white or take rockwool and hold that in place with drywall or mylar. Even just an air gap between inner and outer walls can cut sound significantly, same as an "egg box" surface will help cut sound due to it scattering the sound waves (think of the walls in a recording studio).
When looking at the "insulation" idea, it doesn't have to be a thick layer, think of how much of a difference a foam underlay makes with a laminate floor as an example. Then we have to look at anti-vibration mounts for any and all fans, rockwool around any ducting to deafen any noise from air blowing through it, and then, in theory, you have a cabinet you could put in any room and nobody would have a clue what it was for.
yeah was thinking to use reflective insulation rather than mylar/paint on this one for that reason(plus insulation ofcourse)