So here are the house rules we play with at my table.

I tend to follow the Rules as Written (RAW), sometimes the Rules as Intended (RAI), as makes sense. I’m not big into whole-hog replacing play-tested sub-systems, if only because I’ve seen how easily that can send things heterodyning all over the place.

That said, not all rules are created equal, and things that make for grinding busy-work and management by the player or GM can usually be elided or adjusted when playing with mature individuals who are there for fun.

My House Rules

1. I use Inspiration. I also encourage players to nominate each other’s characters (or call out their own character to me) to receive Inspiration. It’s a fun mechanic to reward special moments of RP or action.
2. Bookkeeping that is no fun is no fun.
   1. I tend to be loosey-goosey about Material spell components, except for expensive ones. (Verbal and Somatic I do pay attention to.)
   2. I tend to be loosey-goosey about encumbrance, unless things look ridiculous.
   3. Keep track of your arrows. I mean, it’s not that big a deal. When guidance is needed, I use the “you can recover half your missiles from any combat.”
3. Dead bodies constitute Difficult Terrain.
4. We play on a square grid. We use the basic “1 square vertical, horizontal, or diagonal = 5 feet” variant in the PHB 192, rather than the someone more accurate “the first diagonal square is 5 feet, the second is 10, the next is 5, etc.” variant in DMG 252, because it’s just simpler.
5. Leveling takes place during a Long Rest. Unless for meta purposes it makes sense to do it some other time. But, in general, “I just realized, I know more spells” seems more suitable to happen overnight than while walking down a path.
6. I prefer Milestone Leveling to getting finicky about XP, dealing with absences from encounters or the table, etc., in ways that leave players unbalanced. Defining adventure goals as the basis for leveling just makes more narrative sense to me, and makes it easier for me and the players.
7. You take a Short Rest as you Long Rest.  So you can be back up some HP if attacked before the end of your Long Rest.
8. I tend to Roll Actives vs use Passives, since VTTs make it trivial to do so.
9. You can use a successful Dexterity (Acrobatics) roll to keep you from going prone when you land from a fall, vs a DC equal to the damage you took (stick the landing!).
10. Flashing Before Your Eyes: Any time you are dying during your turn (other profound incapacitations might apply), the DM (if he remembers or is reminded) will ask you a question about your character or their history. If you answer the question, you get Inspiration.
11. If an obstacle to your ranged weapon is closer to you than to what you are shooting, you can ignore the obstacle (no cover); otherwise, use the cover rules (usually half-cover, AC+2). I.e., a close obstacle can be easily shot around.
12. Ranged attacks with altitude difference: (Discussion)
    1. thrown/twanged weapon at a higher altitude target: the effective range is the sum of the horizontal and vertical distance
    2. thrown/twanged weapon at a lower altitude target: the effective range is the greater of the horizontal or vertical
    3. spell: the range is the sum of horizontal and 1/2 the vertical.  
13. People may be assumed to be sleeping in their armor, unless humor or the DM who has a specific reason for it otherwise make a note that it is not so. Changing out of or into armor is time-consuming and Not Fun. If there are no 5e rules penalizing swimming in armor, we can assume that in this world armor is lightweight and comfortable to wear and sleep in.
    1. In a similar fashion, it’s assumed peoples’ weapons are always with them, unless it is noted otherwise by players or DMs. That would be socially (and logistically) awkward most of the time, but the alternative is a lot of Not Fun moments.

Concluding Notes

Finally, I always try (though sometimes fail) to remember two things about Rules and D&D:

1. D&D 5e is not a physics simulator. It’s not even a great combat simulator. Appeals to reality are less important than verisimilitude (feeling like reality), and both of those are less important than keeping the game rolling along smoothly.
2. The Rule of Cool should always have a place at the table. If someone proposes doing something one-off that is going to be one of those cool moments in a movie that people will talk about for ages … don’t worry about RAW, but remember why you’re all gathered around the table to begin with.