I'm thinking of going back to using different damage rolls for different weapons.
Shocking, I know. I've been a strong supporter of 1d6 damage for every weapon because of its simplicity. But there's not just damage to consider. There's also initiative.
I scoff at most initiative systems. Honestly, why roll? Just give one side a free attack if they surprise the other, then do all the attacks at once, unless one attacker is Hasted or Slowed. If one person kills another, or attacks a spell caster, shortest weapon or lowest spell level goes first, so the victim's attack or spell may be interrupted. Only check this when it matters. (I tried always checking weapon length as my initiative system, but as simple as it was, even it had problems at the table. I sometimes forgot to ask. Fortunately, I gave the players the priority in those cases, anyways.)
But even this could be simplified. Use one of the really simple weapon damage systems: d4 for daggers, d6 for most one-hand weapons, d8 for broadswords, 2d6 for two-handers. Use the damage rolled as the effective speed. A 1-point damage roll goes first, a 12-point damage roll goes last. If checking for interrupted actions, all you need is the dice results on the table right now, or the spell level of any spell cast.
You never, ever have to keep track of initiative that way. It's very temptiing.