I would start with.
Simple Weapon = 1d6 base damage
Martial Weapon = 1d8 base damage
Then modify damage and effects at the cost of comparable tradeoffs. Note, Versatile is equivalent to Twohanded except optionally usable onehanded. Something like.
Die Sizes
1 (minimum) › 1d4 › 1d6 › 1d8 › 1d10 › 1d12 › 2d6 (maximum)
Ammunition (Dexterity only): decrease die size twice
Finesse (Dexterity): decrease die size once
Light (offhand): decrease die size once
Loading: if ammunition, increase die size once
Heavy (medium size only): increase die size once
Reach: decrease die size once
Reach Only (disadvantage within 5 ft): no change
Throw: decrease die size once
Twohanded or versatile: increase die size twice
Examples:
SIMPLE WEAPONS
Ammunitions
Blowgun 1 pierce: ammunition, light, loading
Dart (weighted throw arrow) 1d4 pierce: ammunition, heavy
Light Crossbow 1d8 (!) pierce: ammunition, loading, twohanded
Shortbow 1d6 pierce: ammunition, twohanded
Sling 1d4 bludgeon: ammunition, loading
Axes
Hatchet 1d6 slash: −
Blades
Knife (!) 1d4 pierce: light
Machete 1d6 slash: −
Rods
Baton 1d4 bludgeon: finesse
Cane 1d4 bludgeon: light
Club 1d6 bludgeon: −
Greatclub 1d6 bludgeon: versatile (1d10)
Staff 1d4 (!) bludgeon: finesse, versatile (1d8)
Spears
Javelin 1d4 pierce: throw
Shortspear 1d4 pierce: light
Spear 1d6 pierce: heavy (!), throw, versatile (1d10)
MARTIAL WEAPONS
Ammunitions
Handbow 1d4 (!) pierce: ammunition, light, loading
Heavy Crossbow 1d12 (!) pierce: ammunition, heavy, loading, twohanded
Longbow 1d10 pierce: ammunition, heavy, twohanded
Shuriken 1d4 pierce: ammunition
Axes
Throwing Axe 1d6 slash: throw
Battleaxe 1d8 slash: versatile (1d12)
Greataxe 2d6 slash: heavy, twohanded
Blades
Dagger 1d4 pierce: finesse, light
Greatsword 2d6 slash: heavy, twohanded
Katana 1d6 slash: finesse (!), versatile (1d10)
Longsword 1d8 slash: versatile (1d12)
Rapier 1d6 (!) pierce: finesse
Scimitar 1d6 slash: light (no finesse!)
Seax 1d6 slash: light
Shortsword 1d6 slash/pierce: finesse
Spatha 1d8 slash: −
Sword 1d8 slash/pierce: finesse, heavy (!)
Throwing Knife 1d4 pierce: finesse, throw
Rods
Mace 1d8 bludgeon: versatile (1d12)
Nunchaku 1d10 bludgeon: finesse, twohanded
Throwstick 1d6 bludgeon: throw
Spears
Lance 1d8 pierce: heavy, mount (1d12), reach, versatile (1d12)
Longspear 1d8 pierce: heavy, throw, versatile (1d12)
Pike 1d12 pierce: reach only, twohanded
Trident 1d6 pierce: throw, versatile (1d10)