I have a few houserules, most campaign-specific for immersion.
One I'm trying (had been in effect only for one game so far) is a Dark Souls RPG-inspired initiative rule whereas monsters and NPCs all act on initiative 12. Then, players either roll normally, with advantage, or with disadvantage given the situation. Players immediately know where they stand and the combat starts smoother. Reactions from players have been positive so far.
In our present game we don't care much about equipment but in one of my previous campaigns, encumbrance worked like this.
You have an amount of equipment slots equal to your Strength score. (Dwarves added CON modifier to STR score)
Light items, weapons, and armours weight 1
Medium items, weapons, and armours weight 2
Heavy items, weapons, and armours weight 3
Backpack weights either 1, 2, or 3, in turn affecting the "supplies DC" to know whether you run out of water, food, arrows etc. That part needed work. I'm anxious to get my Level-Up book and see if I can make it better.
In the same campaign, bucklers were considered a 1d4 bludgeoning light weapon (for TWF) and you could spend your reaction to gain +2 AC against one attack. Medium shields were standard, plus you could spend an action to raise your shield for 1/2 cover (+2 AC on top). Heavy shield gave +2 AC and you could use your reaction to gain +2 bonus to Dex saves vs fireball-like spells, and you could spend an action to raise your shield for 3/4 cover (+5 AC on top).