I played for a couple more hours last night...
The negative status effects you can use on your enemies are things like "Weakened," "Vulnerable," "Distracted," "Sluggish," and so on.
On top of this, your characters have four stats apart from HP/PP: Attack, Defense, Speed, and Luck. Attack and Defense are not exactly what you think they are - they are actually Accuracy and Evasion, respectively. At each level up, you get one point to add to any of these four stats.
I have two frustrations in most battles: my characters miss a lot, and at level 6 my characters only have about 8-10 PP each, which is only enough to do two moves or so. Tails has an ability that heals 6 PP over the course of three turns (and costs him 5 PP to use), and you find a fair amount of PP restoring items, but it can get annoying having to restore it constantly. Most characters can learn a move that has 100% accuracy, so in order to hit some of the more agile enemies, you may have to use these moves often and keep restoring PP.
Anyway, what I'm getting at is: at this point in the game, it seems like Attack is the best stat to dump points in to just be able to kill most enemies off a lot faster and easier.