John, alternatives to using an rtc module:
if you have a type of Arduino that has wifi or Ethernet, you can program the Arduino to get the time from a Network Time Sever, then use it's internal timer to maintain the time after that. This will eventually drift away from the correct time, but you can re-sync with the network once per day, for example.
You can get modules that receive the time from long wave radio transmitters.
But an rtc module is probably simplest for beginners. I would recommend a ds3231 module over a ds1307 module, they are about the same price but much more accurate.