I'm just wondering which sorts of units people generally use in the game, at least in the early to mid-game before heros' power becomes out of whack?
Personally, I find it completely useless to construct units. It may simply be that I haven't played a game long enough, but I find that the pre-constructed units are simply more powerful, and since they keep up with the latest armor and weapons, I can't really design anything better. I can't see any use for designing units aside from designing odd utility units for very specific purposes, outside of general fighting units.
Am I wrong that designing units seems to be mostly obviated by the prebuilt faction-specific units, or are people (who actually use units extensively) finding that designed units have been useful?
I may not like the "look" of one unit and decide to give it a look of my choice. And certainly, being able to pick exactly what bits of armour to use, which traits and what weapon can allow me to create versions that suit better my needs. I don't tend to use anything default beyond the basic militia, spearmen and defender (ok, the pioneer is an exception during all the game). From there, it's all custom.
You should do fine with default units but using customs gives you more options.
I am pretty sure the champion stack of doom will be nerfed somehow. If not its not a game for me. Then normal army units will matter.

That's my usual mid/late game army in my games. You may change the Champions and their gear but the regular troops are the same: non upgradeable troops armed with spears and leather armour, in groups, with Fast/Charge/BloodThirsty*.
In this pic's case: Until late game, only my designated mages (the two in the back) could have the time to strike the normal enemies before the troops obliterated them in the (usually) first turn as they can cross the whole map most of the time and can do some nice damage. The poor Othollo, the designated melee champion, had to get the best magical gear, buy a horse and get to level 16+ to actually be able to reach the enemy before my normal troops and be able to maul the enemy. Only against really strong enemies (HP + attack combo) is where my troops don't shine so much (and these days Othollo mauls them to death in first turn anyways, and lately my Sovereign seems to almost instacast Fireball too).
Of course, playing against the current AI in Normal doesn't suppose as much challenge as I thought... yet. But right now, in the mode i play, it works.
* I do make other designs for archers and "defenders" but this is my favourite offensive unit to go along with my Sovereign.
Eidt: Othollo goes the "General" route with Leadership and Tactician, which are great help for the troops (the "mages" focus on magic stuff, of course)