Mint Mobile does not support the Apple Watch.
And with the Family Plan you still need to have an iPhone with a carrier that supports the Apple Watch, as well as a carrier that will work with the Family Plan. That is not Mint Mobile.
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.
Then you could stay with Mint Mobile.