Quiet Components/Configurations
An internally geared system would be the quietest option available for a commuter set up. A groupset such as Rohloff, Shimano Alfine or SRAM would offer near silent operation. You could pair this with a belt drive train to reduce this further. This would also alleviate hub noise. The Rohloff probably has the quietest shifter as it is not indexed.

For brakes I'm not sure if there is any difference between the noise made by rim vs. disc brakes although when they bite they may be louder than a coaster brake but much safer. Disc brakes would be my recommendation if your were considering cycling in the rain. There is no difference in noise between mechanical and hydraulic set ups but for commuting 140mm mechnicals would be just as effective as hydraulic brakes (unless your doing technical descents) as there would be very little differentiation in modulation and they are easier to maintain.

Accessories will be all about what you choose, how you fit them and how you maintain the bike. You will need to keep things well lubricated to keep noise down (anything with a bearing) and taking time to fit things properly and to the right torques (such as bottom bracket). Pumps and tools can be placed in old tubes to keep them from rattling.

For tires I dont think totally slick is the best option, also where you have said rain was an issue but something that had a specifically noise and puncture resistant tread and a low rolling resistence would be best for commuting.