Hello!
Correct, weapons don't matter, but you can "upgrade" them so they provide skill dice when rolling. That translates into increased damage as each success (5 or 6 on check die and 6 on skill die) inflict 1 point of damage. The optional rules include more ways items can be enhanced to provide skill die or even inflict more damage.
There are no rules for unarmed combat at this point. Personally, I would restrict the damage inflicted on the target to 1 hit regardless of the roll. I think that would work well and wouldn't break the system.