In life outside Elanthia-- and in many worlds besides GemStone III-- inventory is arranged logically top-down as the person puts it on.  Unfortunately, in GemStone III, this is not so.

When putting on inventory items, the rule is "last worn first on"-- if you put on a rose and then put on some slippers and then put on a skirt, your inventory will show "You are wearing a skirt, some slippers, and a rose".  If you remove an item and don't set it on the ground or put it in a container, its "presence" will remain on your person, and it will go immediately back where it was initially-- so each item must be put away and then worn again in order to arrange things the way you wish.  In order to get your entire inventory straight, the best thing to do is to either a) put it all on in reverse order, or b) put it all on in the correct order (which will come out reversed) and then log out and log back in.
    Why log out and back in?  For arcane reasons of coding, your inventory will flipflop every time you log out and then back in-- making you "upside down".  This adds one more reason to the list of reasons why it takes more time and energy than most people are willing to spend in order to get inventory ordered and straightened out.

What inventory order is maximally effective?  Lady Brownyng recommends setting things apart into three categories (jewelry, clothing, and containers) and going head-to-toe in each category.  I disagree; I favor going head-to-toe through the entire inventory, so that your belt is actually around your waist and your shoes are the lowest thing in your inventory no matter what.  My normal technique is to take my inventory... hmm, this is going to be simplest if I use an example.

First step: I look at my inventory.

You are wearing a silk-lined suede satchel embroidered with colorful butterflies, a deep crimson wand harness, a velvety deep yellow rose, a fluted golden-scaled lizard, a cavorting gold aardvark pin, some sun-hued velvet dance slippers laced with slender vermilion silk ribbons, a woven wheat lover's knot, some storm grey casting leathers, a diamond engagement ring, a gold-threaded red ruffled skirt, a flame-hued watered silk cloak, a silken garnet-hued bag, an Argent Aspis pin, a silk spell components bag, an intricate silver link bracelet, a brass-linked blue crystal pendant, and a salamander skin pouch.

Second step: I pull my inventory into a Notepad file and break it up vertically into a list of items.

You are wearing
a silk-lined suede satchel embroidered with colorful butterflies
a deep crimson wand harness
a velvety deep yellow rose
a fluted golden-scaled lizard
a cavorting gold aardvark pin
some sun-hued velvet dance slippers laced with slender vermilion silk ribbons
a woven wheat lover's knot
some storm grey casting leathers
a diamond engagement ring
a gold-threaded red ruffled skirt
a flame-hued watered silk cloak
a silken garnet-hued bag
an Argent Aspis pin
a silk spell components bag
an intricate silver link bracelet
a brass-linked blue crystal pendant
a salamander skin pouch

Third step: I rearrange my inventory into the order that makes sense to me when going top-down.  I wear my rose behind my right ear, so it's the first item....

a velvety deep yellow rose
a brass-linked blue crystal pendant
a fluted golden-scaled lizard
a flame-hued watered silk cloak

The lizards sit on shoulders, so that seems the best place for it-- immediately on top of my cloak.

a cavorting gold aardvark pin
a woven wheat lover's knot
a deep crimson wand harness
an Argent Aspis pin
some storm grey casting leathers

Pins and pin-worn items are a bit tricky.  I try to decide precisely where my character wears them, and then place them accordingly-- for example, in this case, I think of the aardvark pin as being used to pin the lover's knot to the wand harness, and then the Argent Aspis pin is on the storm grey casting leathers.  (After all, pins are put on something.)  If items are layered (for example, a bodice and a blouse) I usually put whichever item is closest to the outside first.  The most important question is, "Can you picture it?"  If so, all's going well.

an intricate silver link bracelet
a diamond engagement ring

I usually put bracelets and rings after whatever's worn on the torso and before whatever's worn on the legs-- it seems to work well.

a gold-threaded red ruffled skirt
a silken garnet-hued bag
a salamander skin pouch
a silk spell components bag
a silk-lined suede satchel embroidered with colorful butterflies
some sun-hued velvet dance slippers laced with slender vermilion silk ribbons

I actually cheated a tiny bit here-- that's a shoulder-worn satchel rather than a waist-worn satchel.  However, I thought it looked better to have all the satchels, pouches, and so forth together than to have one higher-- and a satchel worn over my shoulder probably will wind up at roughly the level of a satchel worn at my waist, if you account for the strap.  Also, the length of the description of that satchel is sufficient to cause some difficulty if it's mingled up higher-- better just to put it down with the equally-long slippers.  If I wanted to draw more attention to the satchel, I would wear it in a higher location, but I don't really.

Third step: Given this list of inventory, I begin to put my items in that order.  Each item has to be taken off, put in a container or on the ground, picked back up, and worn again... so first I take off the slippers, put them in my cloak, take them out of the cloak, and wear them, then I take off the satchel, drop it, pick it back up, wear it, then the spell components bag... and so on.  I do all of this in a private room (a locker or my fiance's home) and anything that goes on the ground is picked up again immediately.  Every time I do this, I do run a minor but serious risk... if I lose an item because it's on the ground when a crash occurs, standard policy says that the GameMasters will not replace it.  Having a servant around or someone who can hold items for me works just as well-- I could hand my cloak to Tolwynn for a moment and then take it back again to cause the cloak to "forget" that it ought to be somewhere else in my inventory.  At this point, the result is:

You are wearing a velvety deep yellow rose, a brass-linked blue crystal pendant, a fluted golden-scaled lizard, a flame-hued watered silk cloak, a cavorting gold aardvark pin, a woven wheat lover's knot, a deep crimson wand harness, an Argent Aspis pin, some storm grey casting leathers, an intricate silver link bracelet, a diamond engagement ring, a gold-threaded red ruffled skirt, a silken garnet-hued bag, a salamander skin pouch, a silk spell components bag, a silk-lined suede satchel embroidered with colorful butterflies, and some sun-hued velvet dance slippers laced with slender vermilion silk ribbons.

Check back to the first version.  Doesn't this version make better visual sense?

Building an inventory checklist to arrange item order is difficult because so many varied items exist in Elanthia and because so many aspects of inventory arrangement are complete judgement calls.  However, here's a rough attempt at a top-down list....

helms, hats, kerchiefs, crowns, combs, barrettes, veils, horns, etc.
earrings, earcuffs, fake elf ears, etc.
masks
nose rings
necklaces, amulets, etc.
scarves, bowties, and anything else cloth worn around the neck
lizards, songbirds, beanbag toys, or anything else that perches on the shoulder
backpacks, knapsacks, backsheaths, wings, etc.
cloaks, capes, greatcloaks, jackets, etc.
handbags, shoulder-worn satchels, etc.
weapons harnesses or wand harnesses
bodices, vests, surcoats, etc.
torso armor
shirts, blouses, gowns, etc.
armbands
arm greaves
gloves or gauntlets
bracelets, wrist sheaths, etc.
rings
sashes, belts, waistchains, tails, bellychains, etc.
trousers, skirts, kilts, etc.
thigh sheaths, leg greaves, etc.
tights, leggings, etc.
anklets, ankle sheaths, etc.
socks, toe rings, and other things worn on your feet besides shoes
shoes, slippers, boots, sandals, galoshes, etc.

When considering items without a place above (especially pins, symbols, flowers, and so forth) the most important question is-- "Where do I wear it?"  Place the item directly above whichever item seems most appropriate-- for example, you might place a kilt-pin above a kilt, or a buckle above a belt.  A clasp might go well above a cloak, but it might go equally well above a skirt.  A pin could go above almost any cloth item, and a flower could be tucked into a nook or cranny almost anywhere.  If you wear an item in a way that is unusual (using a scarf as a belt, for example) feel free to place the item appropriately.  What matters the most in the end is what suits you and suits your style.

"What about gold rings and crystal amulets?"  If I'm going to be wearing a gold ring for a while, I try to incorporate it into my inventory-- carefully! (Nothing quite like being hurled half-dressed into steel golems by a preset ring.)  Alternately, if I don't plan to use it more than a few times, I remove it immediately upon teleporting in and stash it in my cloak.  Since I only wear one item above my crystal amulet (the rose) I can simply remove the rose, put it in my cloak, wear the amulet, take out the rose, and wear it again.  Those who are particularly fashion-conscious may wish to dye an amulet or buy an altered amulet and then rub a normal crystal amulet into oblivion-- this would grant you full control over which channels you listen to without being forced to actually wear an amulet.  If you're in the habit of dying often, however, (as I am), this grows a bit too expensive for most to keep up.

Some things repeat well.  If you're wearing two amulets, two bracelets, three sacks, and so on, this is not a problem-- it's clear how it looks and fits together.
Some things repeat poorly.  If you're wearing two cloaks, two pairs of gloves, three bodices, two pairs of boots, four gowns, or anything else in this vein (I've seen most of these-- and even done two), you may wish to reconsider your inventory.  Just because you can doesn't mean you should.  (Of course, you may have your reasons... three sweaters while you're running around Icemule, for example.  But do keep things in perspective.)