For my own in progress neoclone of OD&D I came up with these numbers:
Weapon 20-Sided Die Score to Hit by Target’s Armor Class
Class Type 9 8 7 6 5 4 3 2
0 Unarmed 9 12 10 13 14 16 17 18
1 Dagger 10 13 11 14 15 17 18 19
2 Mace 9 12 11 14 13 15 17 18
3 Sword 7 10 9 12 15 17 19 20
4 Axe 10 11 11 12 13 14 16 16
5 Hammer 10 13 11 14 13 15 16 17
6 Staff 7 10 8 11 16 18 19 20
7 Sword (2-h) 7 8 7 8 12 13 16 16
8 Poleaxe 8 9 9 10 12 13 15 15
9 Morning Star 9 10 10 11 13 14 17 17
10 Spear 8 11 8 11 13 15 17 18
11 Bill 8 9 8 9 13 14 17 17
12 Lance 6 9 7 10 11 13 14 15
Missile Weapons 9 8 7 6 5 4 3 2
Dagger 10 13 11 14 15 17 18 19
Axe 10 11 11 12 13 14 16 16
Hammer 10 13 11 14 13 15 16 17
Spear 8 11 8 11 13 15 17 18
Javelin 8 11 8 11 13 15 17 18
Sling 10 12 11 13 14 15 16 17
Bow 8 9 8 9 15 16 20 21
Crossbow 8 9 8 9 13 14 16 17
All weapons do 1d6 damage, although attackers have the option of doing double damage by taking a -5 to hit penalty (and triple at a -10 penalty). Higher level characters simply add their attack bonuses-4th level Fighting-Men add +2, 7th level Fighting-Men add +5, etc. In general, however, what might translate into extra damage (because the weapon is bigger or whatever) in Greyhawk and 1e is reflected in a higher probability to hit.
There are also additional damage modifiers for combat against large creatures that have more body mass to penetrate. Spears, poleaxes and two-handed swords will get a +2 damage bonus and daggers and maces will suffer a -2 damage penalty, for example.
The function of Weapon Class is similar to that in Chainmail. The higher class always gets first attack in the 1st round, but the lower class may get first attack or even double or triple attacks in subsequent rounds where initiative is tied.
The chart gives a higher value to shields, though their value declines as armor improves. This I think is more consistent with the historical record than the uniform -1 Gygaxian standard. The table yields quite different results (from, say, Chainmail/Greyhawk) as to the value of certain weapons against different armor types. Among other things, one gets a few "heretical" results such as that against an unarmored opponent, a staff is as good as any weapon and better than many, and against plate, a dagger may be more effective than a standard one-handed sword. These results are consistent with my (no doubt imperfect) research on Medieval and Renaissance martial arts.
I have put quite a bit of thought into this but I am of course still open to criticisms or suggestions.
(EDIT: Sorry, it's my first time actually participating in ProBoards-though I've been an avid reader for some time. I didn't realize the formatted table would collapse. I will try to correct it after work.)