You can get the Series 3 or 4 GPS only Apple Watch and it will work normally regardless of carrier.
You can even get the cellular model of either and they will still work except you will not be able to set up cell service on them.
The Apple Watch works with the paired iPhone most of the time. The Cellular connection is only needed if your watch is away from your iPhone and wifi, and you need make and receive calls or send and receive messages on it.
See here for specific details: How to use your Apple Watch without your iPhone nearby - Apple Support