Depending on the mobo size - ATX at guess - you will be looking at mid or full tower units I suspect. Once you know the size then it comes down to cost, additional features and style in that order on a descending scale (if you are like me).
Personally I would be looking at a full filtered case with a fan controller built in, cable management (space behind the "bottom tray" to get cables neat) and how many fans I can add to it. You want to be aiming at an over pressured case (like a balloon with air in it is the best analogy I can come up with) as it massively reduces dust getting into the case since any gaps are pushing air out. Would be looking at twice as many intake to exhaust fans personally.
I really like Fractal Design - the
R6 Tower is a case that may suit but it is not cheap. It does tick all the boxes and more that you specify though. Another option would be the
R5 Tower - slightly smaller but no glass side to it which I prefer. Phanteks also look really nice and again have a lot of features to mull over if you want an alternative and have some good reviews.
After that to further reduce noise then decent fans will make all the difference for a really quiet PC -
Noctua are excellent and would be my choice if you go down that route but again not cheap. If you do get additional fans them make sure whether you need PWM fans or not before buying them.
As you can tell I may have been thinking along similar lines (with water cooling options because I can).
