Using the system in Moldvay Basic is straightforward and easy, and keeps extra math during the game to a minimum - something that I think is a good design goal. Unfortunately it leaves some weapons as obviously superior choices to others, which means less variety of melee weapons get used in actual play.
Here are my house-rules for melee weapons in Classic D&D, which works with my previous house-rules from In Defence of the Shield. A character who is not using a shield may choose to wield either a two-handed weapon, or wield two weapons at the same time.
Wielding a melee weapons with two hands gives an attacker +1 to hit. Long two-handed weapon may use it to attack from the rear ranks. If using individual initiative, a long weapon automatically gains initiative on the first round of melee combat.
Characters fighting with two weapons roll to attack normally. After rolling for damage with their primary weapon, they may choose to re-roll using the dice for their secondary weapon. This second roll is used for damage, even if it is less than the first roll.
Used with the house-rule for shields this means characters will either have +1 to hit, a chance to re-roll their damage, or a chance to block damage with their shield.
Individual weapons provide some minor benefits as well.
Torch - d4
Many animals and monsters are afraid of fire. They will avoid, or possibly need to make a morale check before attacking a character wielding a torch.
Dagger - d4
Club - d4
A club can be used to make non-lethal attacks. Note: A Wizard's staff is treated as a club, rather than a Quarter Staff.
Quarter Staff - d4
A Quarter Staff is treated as both a two-handed weapon and as well as two weapons. This provides both +1 to hit and the option to re-roll a d4 for damage. A Quarter Staff can be used to make non-lethal attacks.
Hand Axe - d6
Lance - d6
This long weapon is always used two-handed if on foot, and one-handed if used when mounted. This weapon does x2 damage if used while mounted and charging, or when on foot and braced to receive a charge.
Mace - d6
Some types of maces (flanged) are +1 to hit against opponents in medium or heavy armour.
Flail - d6
A defender does not make a shield roll when attacked by an opponent with a Flail.
Short Sword - d6
Spear - d6
If a spear is used two-handed it counts as a long weapon.
War Hammer d6
+1 to hit against opponents in medium or heavy armour.
Battle Axe - d8
This weapon is always used two-handed. An additional +1 to hit against opponents in medium or heavy armour. (+2 total for being used two-handed)
Sword - d8
Pole Arm - d10
This long weapon is always used two-handed.
Two-handed Sword - d10
This weapon is always used two-handed.
Hopefully that gives some variety to the list of weapons, without making any greatly over or under powered. Even with just shields and weapons finished, things are starting to take shape! :)