I've not seen anything to address this whole subject officially. The answer from Dark Wanderer is excellent as all of those things are mistakes that you'd learn from after making them. There is no good answer specific to RAW, as 5E is too young to have produced a book addressing the complexity of the Planes of Existence.
If you dig into the Planar material, you'll get bits and pieces that relate to what an afterlife has to handle. Earlier editions have books on this, but know that each has a slightly different cosmology and vary from one another in meaningful ways. For instance, editions have flipped functions of the Ethereal and Astral Plane and which one is a path to the outer planes. I"ve tried to address this myself and I find there isn't enough meat in 5E. I find it convoluted as the pieces feel as if they weren't designed with the idea of all working together. Going back to other editions for source material--leads to some more confusion.
Since 1st edition AD&D, the outer planes match a spectrum of alignments--some of which did not exist in the game. There are 8 non-neutral alignments, but there are 16 outer planes, with half-steps between each alignment--half steps that do not exist in the game. In 5e, they overlap two alignments, like a DMZ between alignments. They mostly re-used names of various early European "heavens" and "underworlds" (valhalla, olympus, etc). By 5e they generalized them somewhat (Arborea, the Olympian Glades of Arborea, CG; DMG pg 58) But if you don't use these pantheons... the names become more meaningless. And are all Greek gods ChaoticGood? Olympus was the home of all the Greek gods. It is a confusing subject. SO don't hesitate to move away to something that makes better sense. It is the afterlife, it doesn't have to make sense to the living.
5E DMG pg 43 starts the discussion about the Planes. In addition to some flavor and mentions of places from past editions, they provide some possible effects on living characters that travel to the planes. The book is quick to say make this into your own.
But you're concerned with the dead not the living traveling there... the 5e books give you some referential ideas if you read through stuff.
In 5e The Prime Material Plane has three overlapping planes of existence. Think of it like phases in Star Trek. You change your phase of existence and shift into the Shadowfell or Feywild or Border Ethereal. Your body moves into that plane, but you are still where you were in the Prime. When you go ethereal, you see the material world you left around you. However, your body is converted to etherealness... incorporeal-just like ghosts. If you phase into the ShadowFell or FeyWild there are corresponding landmarks that relate to the same place in the Material world (and your physical body comes with you). FeyWild has evil and good creatures and regions. Shadowfell is only undead and evil. They are supposed to be echoes of the real world--but the design was more flavor than symmetry. For instance, the Shadowfell has gates to evil outer planes, but Feywild doesn't mention any access to the outer planes.
I am certain that I read that souls travel to the Shadowfell when they die. I can't find that in the DMG. This was true in 4E, maybe I'm imposing old editions on new. In 5E the portals to the shadowfell overlap where spirits and death lingers, such as battlefields, graveyards. So this sounds like there is a natural transition tendency to the ShadowFell at death.
Now the confusion for me in 5e, is that the Ethereal is not where your soul goes/exists, despite ghosts and specters being ethereal beings. In 5e, the Astral Plane is an infinite plane with no size. DMG.46, "visitors travel as disembodied souls to reach the outer planes." Pretty much sounds like this is where you go when you die. The Astral Plane is the realm of thought and dream (DMG.46) The Ethereal does not get you to the outer planes as it did in previous editions. Astral projection, PHB 215, sends your "soul" (astral body, consciousness) to the Astral Plane but leaves your body behind with a silver cord linking your soul to your body. If your astral form dies... 0 HP , you go back to your body via the cord. Cut the cord, your "soul and body are separated, killing you instantly." The vagueness here is "killing you," which you? Astral Soul "you" as well as your physical body? Death of the body is definite. But whether this kills your astral body/soul is the question for me. In previous versions, it killed the body and your Astral form was left to wander.
The weird part--which has always been confusing--is if you travel to another plane via a portal in the Astral Plane, your body is transported through the cord to the Outer Plane you travel to. This is how Gate works, you step through with your body. If you gate to the Astral Plane, your BODY moves to the Astral Plane as well--no cord. These two different forms of existence within the Astral has existed since early editions. The flavor of astral projection conflicted with the concept of just stepping into it. Also the Gith physically live in the Astral Plane, where you can find corpses of gods.
Maybe the Ethereal might be thought of as where lost souls wander the prime material? It does have portals in the Deep Ethereal to the other INNER planes.
The books skip what the function of the Ethereal is in this edition. It has to for some monsters.
MM has bits and pieces in demons and devils, particularly about Lemures and contracts of owning a soul. Night Hags are a little confusing as they ethereally straddle a sleeping victim and invades their Dreams with a Nightmare Haunting Action. (Thoughts and dreams are Astral subject matters). So here the Ethereal plane is just there to ghost-walk through the world. The haunting can kill the victim. The hag tries to corrupt their thoughts and get them to commit evil acts when awake. If they do and the subsequent hauntings kill the victim, she traps their soul for transport to Hades.
It really is too big a subject for the core books. But the above are the official tidbits that I recall touch on the subject.
You really will have to homebrew it or borrow modified ideas from previous versions. Personally, I like the previous versions where the Ethereal was a ghost realm, overlapping all the Inner Planes and the Border Ethereal was the edge where you transitioned to the Outer Planes. The Astral Plane was solely a plane of mind and thought, never referring to the soul. Then the Gith started physically living there, god corpses... it got confusing too.