Unarmed damage for a monk is a bit different than for other classes. A monk that has armed a simple weapon can still gain the benefit of being "unarmed", but they are limited to rolling the monk's unarmed damage die when doing so. At low levels this is less, but at higher levels this is equal and eventually even more than the weapon's damage roll.
pg 78, PHB Monk, Martial Arts Section.
- you can roll d4 in place of normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels.
This includes the quarter staff, which is both a simple weapon as well as versatile.
phb pg 147. Versatile - This weapon can be used with one or two hands. A damage value in parentheses appears with the property-the damage when the weapon is used with two hands to make a melee attack (That's 1d8 for quarter staff)
So the first attack can be done two handed for 1d8 base damage, but following monk bonus attacks must slide to one handed and you do damage with monk's unarmed damage roll (not the weapon's damage dice).
For the first attack, roll damage as a two handed weapon, the second and subsequent damage rolls, roll as a unarmed monk weapon. This gives you 1d8+DEX, 1d4+Dex, 1d4+Dex at low levels.
When you reach 5th level you can also attack or strike 4 times (that's right, check out the block quotes below)
phb pg 79 extra attack Begining at 5th level, you can attack twice, instead of once whenever you take the attack action on your turn.
Note this does not cost a bonus action.
phb ph 78 flurry of blows Immediately after you take the Attack action on your turn. You can spend 1 ki point to make two unarmed strikes as a bonus action.
That's right, so after level 5, your attack sequence is (not including str or dex bonuses) 1d8, 1d8, 1d6, 1d6...wow. If you added Fangs of the Fire Snake to that attack, you can add a 1d10 fire
Damage to EACH strike if you spend the ki (need to spend 1/hit). That can one shot some boss monsters now and again.
Eventually as you gain levels you attacks will get stronger as well as gaining new effects. You unarmed damage is going to exceed many weapons damage, and you'll be able to stun or knock prone pretty early on compared to other classes. This is VERY useful.
My gaming group thinks monks are over powered, not underpowered. Our group has between 25 and 30 people spread across 4 tables so we have a good mix of and exposure to pretty much every class and archetype out there.