we pay any extra for phone service to use the watch with cellular?

You will have to pay your phone cellular carrier money to have the Apple Watch with cellular, but. If you decide you don’t want to have cellular, or you don’t want to pay for it anymore, you can cancel the plan and use the watch as GPS only. You will always be able to add the cellular back if you want to.

The GPS only Apple Watch can do Everything the Cellular model can do AS LONG AS your iPhone is nearby, where nearby is generally somewhere in the same moderately sized home. The Cellular model allows you to leave your iPhone at home while you go for a walk, run, bike ride.

Use your Apple Watch without your iPhone nearby - Apple Support

If you decide you want to be able to leave your iPhone at home and still have connectivity, then

The Cellular + GPS Apple Watch has an eSIM and 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:

Apple Watch - Carriers - Apple