It depends on how good your weapons are, and how good your kung-fu is.
Making multiple attacks is the key, and there are two rules available to obtain them. Two weapons fighting (PH p.195)...
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
...and the Martial Arts class feature (PH p.78):
When you use the Attack action with an unarmed strike or monk weapon on your turn, you can make one unarmed strike as a bonus action.
Note that the bonus action unarmed strike granted by martial arts still adds the ability modifier to damage.
The relative merit of armed and unarmed attacks depends on how much damage an unarmed attack does, and this depends on Monk level: 1d4 at level 1, 1d6 at level 5, 1d8 at level 11, etc.
Presuming your Dexterity is higher than your Strength, your reasonable weapon options at level 1 are as follows:
- Use a pair of light weapons (e.g. shortswords) with two weapon fighting. This does 1d6 + Dexterity, and 1d6 as a bonus action obtained from two weapon fighting.
- Use a versatile weapon (e.g. spear or quarterstaff) in two hands to do 1d8 + Dexterity, and 1d4 + Dexterity as a bonus action obtained from martial arts.
Use no weapons, doing 1d4 + Dexterity twice.
Assuming a Dexterity modifier above zero, the versatile weapon is the best choice.
Level 5 Improvement
At level 5, a Monk gains the Extra Attack feature and an increase in martial arts damage to 1d6. The situation is now:
- Pair of light weapons: 1d6 + Dex (attack), 1d6 + Dex (extra attack), 1d6 (two weapon fighting bonus action)
- Versatile weapon: 1d8 + Dex (attack), 1d8 + Dex (extra attack), 1d6 + Dex (martial arts bonus action)
- No weapons: 1d6 + Dex, 1d6 + Dex, 1d6 + Dex
Level 11 Weapons start to become an option rather than requirement
At level 11, martial arts damage increases to 1d8 and matches the versatile weapon for damage.
Either way, you don't need to be unarmed to obtain the damage provided by martial arts, as described in the PH p.78.
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels, as shown in the Martial Arts column of the Monk table.
Damage isn't everything. Using a versatile weapon in both hands means you don't have a free hand. Here are some abilities you give up:
- The level 3 Monk class ability Deflect Missiles (PH p.78) grants a free ranged counterattack if you have least one hand free.
- Gloves of Missile Snaring (DMG p.172) require a free hand to function.
You have greater freedom to interact with an objects. For example, switching to a ranged weapon doesn't require first sheathing or dropping a melee weapon.
All the comparisons to this point make the assumption that you only have access to mundane weapons. Clearly, the bonuses to attack and damage for magic weapons will tip the scales back in their favor. It's something of an arms race between the Monk's improving martial arts damage, and the bonus to attack and damage for increasingly rare and powerful magic weapons.