The best way I found to handle this was to create 'to hit' tables specific to each character in the party. Instead of cross referencing a fighter table to figure out if 'Black Joe' hit AC 3 after adding up all the modifiers, you instead created a 'Black Joe' table which cross referenced his sword +3 vs. each AC. Then, all you needed to know was the dice throw and any temporary modifiers because his strength, magic sword, and the long sword vs. AC modifers were already calculated. Ditto for Black Joe's short bow +1, his backup dagger, and his unarmed attack.
It was a small headache to prepare the tables, but it saved an enormous amount of time in play and made using the 'weapon vs. ac' modifiers no harder than not using them. And once you had the tables, they were really cool, because suddenly the game started to make sense at a tactical level. Realism jumped up enormously. You could see that a whip or a unarmed attack were virtually useless against an armored foe (as you'd expect). A heavy weapon designed to penatrate armor was great - if the foe was armored - but suffered compared to a finesse weapon against a lighter unarmored foe. Your longsword, damage king though it was in most cases, could have real issues penetrating something as protective as plate so that there really was reasons to consider using other types of weapons. It wasn't obvious which weapon was best.
As for the AC of monsters, you didn't have to calculate them all in advance and you really didn't have to concern yourself too much with what AC the monsters hide had. Instead, you decided roughly what dexterity the monster had, and then the rest of the monster's AC translated as armor by necessity. This seems like its just as hard, but figuring out if the monster ought to qualify for non-armor AC seemed easier to me than figuring out what armor it had. So, if the monster had an AC 4, but didn't seem particularly agile, that was obviously all armor. Or, if the monster had an AC 2, but was a small lithe fairy, then perhaps that was all 'bonus' (size, dexterity, swiftness, magical enhancement), and its AC was 10 (with a AB of +8). Once you decided for one monster, you just made a note and then you 'knew' and could write it in a stat block (which was like 2 lines back then) when prepping for an evening. And you were really unlikely to introduce more then two or three new monsters in a session, and after a while it didn't much come up.
No, the real complexity - and one that I had just started to consider - was what weapon did the monsters attacks qualify as? Near the end of my 1e career I started making specific monster vs. AC attack tables to go with each monster entry.