As you describe the way you want to use your Apple Watch, then yes, you have to pay for cellular service on the Apple Watch.
If you get a cellular Apple Watch And you decide to enable the cellular radio, then the Apple Watch shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:
https://www.apple.com/watch/cellular
If you get a GPS only Apple Watch, or you do not activate the cellular radio, then the Apple Watch can do Everything the cellular model can do As Long As your iPhone is nearby. Where nearby is say in the same moderately sized home.