Apple Watch series 4

I don't believe AT&T allows the cellular watches on prepaid sims. Only on contracts.

For setup see here: Set up cellular on your Apple Watch - Apple Support

You just need to select the "Setup Cellular" option while setting up the watch, and follow the onscreen prompts.

The iPhone and watch need to be using the same carrier. The watch actually shares the cell service from the iPhone, and its assigned number.

You cannot set up a watch with Sprint if your phone is using AT&T.

Beyond that, yes, you can buy it from Sprint, and then set it up with AT&T on your iPhone.

With that said, why do you want to buy it from a carrier you aren't using?