Which faction do you like the most in Heroes of Might and Magic IV?

Well, I doubt that's the kind of list they had in mind.)))

Although, I still don't understand why you would pump up the Archer's skills. A Ranger, maybe, since they focus more on scouting than combat, but why specifically the Archer?

The Archer is not a class; it's a hero. And he's focused on combat. He doesn't level up his archery skills; he levels up his combat and melee skills. After getting Grand skills, you can level up magic resistance in both areas.
Why him specifically? Because he has the highest chance of getting a melee Grand skill earlier than any other hero, except for the Barbarian. And "filling" the skill tree with magic and other skills is like a death sentence.
Why? That's an interesting question. On maps that are too "tanky," it's probably not necessary. But on the 2nd week, a good fighter with support (a life mage with healing, a nature mage with buffs and summons to remove debuffs) and a couple of Imps will take down much more than all the troops combined. :)
A fast hero is definitely needed, except for very small maps. There's no arguing with that. :)