Using Arduino as basis of a synchronized clock system

I am a new user, I have searched for topics covering my post. There are a couple of threads that peripherally address some of my questions.

Synchronized clock systems are frequently used in, for example, schools so that all classrooms display the same time and often the master clock will ring bells to signal events. I would like to enhance the functionality beyond just displaying time, but displaying time will still be the primary purpose.

I won't go into the specifics of different sync schemes here, in general they are AC voltages pulsed through a relay.

I have two preliminary lists of functions I need.

Master clock

  1. Act as wired master clock
  2. sync wired
  3. impulse
  4. Ethernet
  5. POE
  6. act as wireless master clock
  7. ZigBee
  8. 802.15.4
  9. programmable
  10. USB
  11. Ethernet
  12. Wireless
  13. Web page

Secondary clock

  1. Act as wired secondary clock
  2. sync wired
  3. impulse
  4. Ethernet
  5. POE
  6. act as wireless secondary clock
  7. ZigBee
  8. 802.15.4
  9. display time full color
  10. hours minutes
  11. minutes and seconds
  12. seconds
  13. display messages full color
  14. display
  15. LCD
  16. LED matrix
  17. ?
  18. projector
  19. USB Programming

Ok, start with a DS3234 SPI Clock module for accurate time keeping, or a GPS module for satellite time, and go from there. Arduino can do all the things you list. Different folks will implement them different ways.

I completely forgot the smartwatch. Any recommendations for the microcontroller board?

Well, if you're talking ethernet & POE, I'd start with one that has support for that.