Do you want a clock or a receiver to monitor?
In the former instance, look for "atomic clocks." They are cheap and are a typical clock that periodically (e.g., once a night) captures the time signal and self-correct.
If you want to build a receiver, consider 4 options:
1) Harvest one from an atomic clock
2) Buy a kit. They used to be common (e.g., CMMR-6), but that source has dried up. Here's another source:
http://www.auroralchorus.com/wr3gx2.htm3) Buy an SDR dongle/receiver
4) Roll your own. See SID image
I did all four and the journey was fun, particularly writing the code to decode the signal, which in the US is WWVB. Attached are pictures of my antenna, receiver decoder, and a simple schematic.
Once the fun was over, I just bought a very inexpensive "atomic" clock and keep it next to my workbench.