I have pipe dreams of running some Swords & Wizardry this summer. Although I have a copy of S&W complete, I've been thinking about "White Box" style damage, but with some caveats.
Some of the common rules I've seen and liked have included:
-Two handed weapons roll 2d6 and take the best, with the exception of the quarterstaff.
-Dual wielding characters receive +1 to hit.
-Damage based on class, allowing any character to use any weapon.
Some other things I'm considering as well:
-Fighters (and fighters only, no sub-classes) receive a damage bonus based on level. (+1 per so many levels, maybe every three?)
-Everything does 1d6 damage, but fighters get to roll twice and take the best. (In this case, two-handed weapons would probably just do +1 damage instead of best of two... rolling three and taking the best of two has a certain clunkiness to it that I don't like)
-Weapons have conditional bonuses and penalties based on things they are good at/things they are not so good at. For instance, daggers are good at fighting in close quarters such as an alley, pole-arms are good for fighting in an open space. In favorable circumstances, a weapon receives +2 to hit, and -2 in unfavorable circumstances. This requires a lot of on-the-fly rulings or else bookkeeping for what weapons is good for what and not-so-good for what. Eew. I can see the appeal, but I suspect keeping track of it will be unwieldy, plus I'll have players constantly trying to bullshit me. :) ("A troll's leg is kind of like a tree, and axes are good at cutting trees down, so I think I get the +2!")
I stole this idea from a post by Vincent Baker around ten years ago, although he was talking about firearms in games.
-Give every weapon one special ability.... so maybe flails ignore shields, crossbows treat armor as one category lighter, etc. Again, this is slightly book-keepy, but not as bad as the previous idea.
Given that I'm all about the simplicity lately, I'll probably go with either fighters roll damage twice or one of the options from the first bunch. Historical simulation is at most a tertiary goal of mine when I run D&D, after all.