By default, routers will try to balance, be it chests, barrels, or anything else among those lines.
I usually just put 1 stick in all the barrels that are empty, because sticks are not something you should find too much while mining.
The major down part of the routers is that, without the upgrade, you can't safely have an overflow/misc chest.
And before you ask, no, I don't remember what s the module to prevent it from trying to put the same amount everywhere.
So that means that you might have to filter the items that go in the router before hand.
Might not exactly be what you where looking for.
I would suggest trying out the router and its upgrades in a test world (spawn yourself what you need in there), because this thing can really be a massive help in other automations too, not just sorting into barrels.