In the 1974-style (now up to 1975-style, as it's been running more than a year, so we've brought in some of Greyhawk, and more recently, some of Blackmoor) OD&D game I've been playing in for a while, we've used d6 damage the entire time. The DM normally rules initiative situationally, but in general, in the first round of combat or as opponents close into melee, longer weapons always get first attack. Once combatants are engaged at close quarters, shorter weapons normally get first attack, and may qualify for multiple attacks if the enemy's weapon is particularly long and thus cumbersome.