What's the strongest pet/minion based class in this game?
Necro, by far. Beastmaster has some cool stuff but falls behind and you want to be on the frontline with the beasts. Necro can just sit back and relax.
And Necro has lots options to choose as summons. Bone golems, skeleton warrior, archers, magi, volatile zombies, wraiths and abominations. Only real downside is the summon AI.
I personally prefer Lich in this game with low life stuff. I melt even bosses in seconds without decent gear. But it's a very risky play style.