I'm trying to get straightened out what to aim for and what to avoid in the breeding of my pets, and the most longterm goal to breed towards seems to be the battlefield.
I feel out of my depth trying to aim for a system that is still so confusing to me, but most importantly - which stats do or do not matter in the battlefield?
Would I be correct in assuming only genetics and the choice of tactics, along with luck on the dice matter? That my bite-blow-rush damage is meaningless there, and that my general stats do nothing but enable certain tactics?

You're completely correct. Individual pet characteristics are used only for unlocking and enchancing certain maneuvers provided by genetics. Individual pet battle stats aren't taken into account at all.

Thank you very much, that helps a ton to know early on. (: