Hello, welcome to WolfPlay! ^-^
I make most of my mushrooms by exploring, which you can do with any wolves that have the "Explore Wolf: Yes" option. Wolves will gain BE {Battle Experience} and will gain better moves that do more damage. You can also level up in explore. Every 10 levels that you complete, you unlock the next area. Some might say that exploring isn't the best way to make mush when you can breed or make art, but hey, I made it relatively far without selling wolves or art.
As a side note, you can also write wolf bios for people for mush. I do, as well as exploring. It may take a while to get popular, and mush income can be somewhat low depending on how much you charge, but if you enjoy writing things with prompts, then I suggest that for making mush.