Most perennial mints aren’t perennial in Alaska. There is an Alaskan variety which is perennial (and it is, typically for the genus, wildly invasive) and the ginger mints (Mentha x gracilis, a hybrid of arvensis and spicata) occasionally survive our winters. Both of these flower in the axils, rather than at the terminus.The rest are annuals in our climate, though they can be transplanted to the garden far earlier than most plants, and continue growing until buried in snow.
I generally buy plants of named varieties and plant them in a raised bed where they have only each other to compete with. Here are a few of my favorites: