Compatibility of Consumer Cellular Phone Service with Apple Watch Series 3 and 4

You should find the list of networks which support Apple Watch GPS+LTE versions with standalone cellular at https://www.apple.com/watch/cellular/

If your network does not support the cellular version you can still have an Apple Watch without cellular, linked through your iPhone. This is the default connectivity even for the cellular version when the iPhone is within Bluetooth range, and it will work anywhere (worldwide) where your iPhone has data service.

There's 2 versions of the Apple Watch. GPS+Cellular and GPS only.

The GPS only version can work normally regardless of what Cellular company the paired iPhone is connected to.

The GPS + Cellular version does require a cell service company that supports that watch to activate it on its service so it can place and receive calls and and send and receive messages when away from the paired iPhone, and not connected to Wifi.

Consumer Cellular does not appear to support activation of the GPS+Cellular Apple watch on their service at this time, so a GPS+Cellular watch will work like a GPS only watch. It will not get calls and messages unless its nearby the iPhone or it is connected to Wifi.

The Apple Watch Application itself on the paired iPhone has no relation to the carrier, so will work regardless.

What region are you located and which version are you thinking about (GPS or GPS+Cellular)?