What class of armor should my party members be wearing?

Fatigue does matter, even on characters you don't control directly. Especially when you need Alistair to shield bash that ogre who's holding you up.

The armor you equip should depend on the role the character plays. Mages and Archers for example, are ranged characters who shouldn't be in the middle of things. They should be wearing light armor and robes respectively. Tanks should be wearing the heaviest armor they can find (massive, basically) so that they can draw the enemies towards them and away from the squishy characters.

Melee rogues should have enough defense that they barely get hit at all, so light armor is the best. I'm not sure about melee warriors with a damage dealing focus, never played them.

I haven't found a use for medium or heavy armor, always going with light or massive for fighters, and robes for mages. Especially since all the good armor sets are massive.

Fatigue is the mana pool for non-mages. It's used to power effect like Dirty Fighting, Shield Bash and so on. Characters that run out of fatigue are reduced to basic attacks. So yes, fatigue matters.

Generally speaking, equipping the heaviest armor a character can wear is a good idea - you'll get more damage absorption. The tradeoff, of course, is a reduced fatigue pool.

IIRC, you can mitigate fatigue penalties by equipping matched sets of armor - multiple pieces of the same kind of armor give a "set bonus" that reduced fatigue.

Fighters are easy; wear the heaviest stuff you can - which should be Massive by the midgame.

Mages can stick with robes, unless you unlock Battlemage and take it - then you can wear heavy armor. I finished the game with Wynn in plate.

Rogues are where the tradeoff between lots of fatigue to power effects and heavier armor to reduce damage gets interesting. I found myself opting for medium armor - I found that it increased survivability of my dual-wielding melee rogue.