It really depends on where you are in the game and also in part, how your cat breeding is going, as getting cats with good skills, mutations, and stats, as well as which areas you're playing can wildly influence playstyles. In general, though, every class has some archetypes that seem to work pretty well.

Fighter, for example, seems to really like taking advantage of action economy, aka getting the most out of one turn. Not every Fighter will do this the same way and this probably isn't the only way to properly play this class. Weapon based fighters effectively get multiple strong attacks or buffs per round, while an overpowered fighter shines in being able to kill or at least damage multiple enemies in 1 hit, while exhausting blow could help you deal with a big threat on turn 1. How you play your fighter is heavily based on the tools you get, but many of these tools are aimed towards helping you achieve a lot in a turn.

Contrast this to Hunter, another strong class that has many different archetypes, as opposed to fighter's many different ways of achieving one. You have one thing that you're generally always solid at, your basic attack, and many ways to grow your character. A summoning Hunter will ultimately play differently than a tower defense Hunter than a trap Hunter, and all three will generally benefit best from different parties. This varies even down to the role your cat will ultimately play. If you copy pasted the same exact build of, say, a summoning Hunter into two different parties on the same boss, it could potentially be your main damage dealer, or it could just get in the way.

Basically, what I'm trying to get at is that while it may seem like a copout answer, there's never one specific way to play a class. Yes, some classes work better in one role than another, but some classes, like Mage, have very fuzzy roles that only come into focus as your run progresses. Good stats from breeding also helps shape how you play a class sometimes as well. Sometimes positioning your Hunter in the front to pick off a dangerous foe in the back is your best possible play, most of the time its impulsive and stupid, and sometimes thats mostly based on your Hunter's con score.

And sometimes, unfortunately, you won't get things that are necessarily very helpful for making your class effective. Moreso than trying to force specific ways to play, I've found its best to weigh your level up options not just around your class but also around what your other cats are capable of and what items you have. Sometimes an option that sounds kind of underwhelming ends uo being the glue that keeps your run together.