Not that pet battles aren't useful, of course, they're just not directly contributing to your character in the same way as reputation grinding. And they're hopelessly addictive, unlike doing daily quests and other reputation grinds.
So, let's get started. I actually think the default interface for reputation monitoring is quite good from Blizzard, as it's a feature that's existed for a really long while, I suppose they've had the time to get it working well. But there are always ways you can improve on it!