Cell phone advice (The Hague)

I am considering a move from the US (NC) to The Hague to begin a job January 1st. I currently have an iPhone 5 and use Verizon as my provider. I have done some research on cell phone providers but am a bit confused about how to stay in touch with family in the US and Canada and also have a phone for the Netherlands and any travel I will do around Europe.
Any advice would be greatly appreciated.