There are a lot of optional rules that you can apply to D&D5 to alter the game slightly to make it feel more like one previous edition or another. Since this is playing in an AD&D module, I’m choosing to use the optional rules that make it more closely resemble AD&D, while NOT using the optional rules that make it more like D&D 3, 3.5, or 4. The only exceptions to this are Alignment and Morale, which I never particularly cared for in any edition; I think the backgrounds in fifth edition work much better to guide role-play than alignment, and if I can’t decide when monsters quit a fight, I shouldn’t be a DM.
Most of these won't have much of an effect on normal game play, as they cover edge cases or special situations in combat. I also plan to point them out as the situations arise (it's my job). But I will elaborate them here for your reference, because I don't want any player to ever NEED the DMG.
The following optional rules from the PHB and DMG will be used:
Combat option: climb onto a bigger creature – DMG 271:
Smaller creatures can jump onto and cling to larger creatures. To do so, they make an opposed check: Athletics or Acrobatics vs the target's Acrobatics. While clinging to the target, the smaller creature has advantage on attack rolls against that target, and can climb around on the creature. The larger creature can make opposed checks to remove the smaller creature: Athletics vs. the smaller creature's Athletics or Acrobatics.
Combat option: disarm – DMG 271:
Declare that you are attempting to disarm your target, then make an attack roll. This is opposed by the target's Athletics or Acrobatics.
Combat option: overrun – DMG 272:
Push through a hostile creature's space, using opposed Athletics checks.
Combat option: shove aside – DMG 272:
A variant of the shove attack: roll a shove with disadvantage. Succeed and move the target to one side or another.
Combat option: cleaving through creatures – DMG 272
Hit an undamaged creature and reduce it to 0 HP in one attack, you may check to see if the attack roll also hits an adjacent creature. If so, apply any remaining damage to that creature.
crafting magic items – DMG 128
Rules for crafting magic items. This is more likely to come into play as NPCs fulfill player orders, rather than the PCs making their own items.
equipment size – PHB 145
Equipment from downed enemies may not fit every PC.
fear and horror – DMG 266
There are some situations so awful that characters will have to perform WIS or CHR saves to avoid getting Frightened or Mad. Unlikely to occur in this adventure.
healer’s kit dependency – DMG 266
In order to use Hit Dice to heal, a healer's kit must first be applied to the wounds.
slow natural healing – DMG 267
You heal naturally only through using hit dice.
inspiration – PHB 125
You do something that makes sense for your character's personality traits but which isn't in the best interests of the character, you get a point of inspiration. You can then cash in that inspiration to get advantage on a d20 roll.
injuries – DMG 272
A critical hit or dropping to 0 HP has a chance of inflicting a lingering effect on the character, which then becomes an additional flaw that the character can incorporate into role-playing. The chance from a critical hit is 10%. The chance from going to 0 HP is 40%.
milestones for additional XP – DMG 261
I will grant XP for achieving objectives/accomplishing tasks in addition to defeating enemies in combat.
mixing potions – DMG 140
Drink a potion while still under the effect of another potion, and there's a chance that something...weird will happen.
more difficult magic item identification – DMG 136
Figuring out a magic item's properties requires using identify or experimentation, not just 'attuning' to the magic item overnight.
multiclassing – PHB 163
Players may choose another character class when leveling, assuming a class trainer of the requisite type is available.
planar effects – DMG 50
When traveling to other planes of existence, characters experience...weird effects.
scroll mishaps – DMG 140
When you attempt to cast a spell from a scroll and [i]fail[/u], something weird happens.
skills with different abilities – PHB 175
As the situation requires, I may ask you to do a skill check using a different ability score than the default.
SpaceSeeker 19's Travel Rule with Mounts (read it on Gamer's Plane)
Mounts increase the distance you travel per day.
training to gain levels – DMG 131
When you earn enough XP to gain a level, your HP and attack modifiers go up immediately if you are gaining a level in the same class. But any other gain of new abilities - or gaining a level in a new class - requires that you spend some time with a trainer in the class to learn the new abilities. This almost always requires returning to town.
variant backgrounds – PHB 130-136
Pretty much every background in the player's handbook has a variant background: the pirate, the knight, the gladiator, etc. These are all available for players to choose during character creation.
The following optional rules from the PHB and DMG will not be used. I am not going to elaborate on them here, unless people ask about them.
alignment – PHB 122
feats – PHB 165
mark – DMG 271
Alternatives to epic boons (won’t come into play anyhow) – DMG 230
point buy for ability scores – PHB 13
encumbrance (D&D5 base rules are sufficient) – PHB 176
firearms, explosives, alien technology – DMG 267
healing surges – DMG 266
hero points – DMG 264
hitting cover (I’ll determine this myself, not using this mechanic)– DMG 272
honor – DMG 264
initiative variants – DMG 270
level advancement without XP – DMG 261
loyalty – DMG 93
massive damage – DMG 273
morale – DMG 273
only players award inspiration – DMG 241
piety – DMG 23
playing on a grid – PHB 192
plot points (I’m happy with suggestions from players, but not the mechanics) – DMG 269
proficiency check variants – DMG 263
proficiency dice – DMG 263
renown – DMG 129
rest variants – DMG 267
sanity – DMG 264
spell points – DMG 288
variant human traits (naturally, since feats are out) – PHB 31
wands that don’t recharge – DMG 141
Edit: I added a percentage chance for the injuries; RAW, the injuries just happen or are up to the DM's whim. I prefer to make it a percentage chance.