I played 1e, and the methodology I eventually evolved to as the fastest method of play was to develop a 'to hit' table for each player in the part that summed all their standard modifiers. That way, the player could just report the result of the roll, and we didn't have the six second delay where they add their strength bonus, magic item bonus, weapon proficiency, etc.
Even better, this meant that I could roll into the table all the individual weapon versus AC modifiers as well, with one line for each weapon a player was likely to use. I ended up clipping hand written sheets to my DM screens, because the custom tables specific to the party actually in front of me were far more useful than general ones.
While it meant a small amount of upfront cost, the results in play were awesome.