There are so many Intel processors that I spent two hours alone trying to decide what I want. I decided at the end of the 4770S. He is in my opinion the most powerful freely available processor for a silent PC. The 4770S has 4600 installed, the most powerful on-board graphics solution HD Graphics. The letter "S" at the end marks the processor as a "low power" = "low waste heat power". There are still ultra-low-power versions, but these have only clock frequencies well below 3GHz. Taken all together you get with the 4770S in the boxed version (ie with the enclosed fan) an almost completely silent combination of graphics processor and CPU, which is extremely powerful nevertheless. If you still a quiet power supply (I have a Be quiet BQT E8-400W) to take and an SSD you get enough a virtually noiseless computer anyway the highest standards. More power is needed only for a hardcore gaming PC and is virtually silent unfeasible.
A small note at the end: The heat sink has already applied thermal grease (looks like gray plastic pads but is soft paste). You have to make sure that you do not lubricate this somewhere during handling.