And why. My character:

Spellbreaker(best shield of the game. Makes wards obsolete)

Ebony mail(best cuirass of the game in my opinion)

Regarding the other three pieces of armor, i have one piece of heavy armor and two pieces of light armor(to raise both skills). I use archery, carry weight and boost heavy armor enchantments

Saarhal amulet

And a fortify health golden diamond ring

Regarding weapons

Obviously a crossbow and secondary a bow with paralysis enchantment

An enchanted with fire damage two handed warhammer

Dawnbreaker

and Mehrunes razor

IMy character has a tendency for daedric artifacts but its obvious why..

My character's 'heaviest armor' tends to be several colors of college robes with light boots (such as college, hide, scaled) and light bracers (like hide or scaled). She also has several colors of the (mod) Triss outfit (non-armor versions). Oh, and she likes to wear a silver and moonstone circlet (enchanted with some extra magicka) because it looks pretty.

As far as weaponry, that's even simpler: Bound/Mystic Bow - it is the only weapon of any type that she will touch. Seriously, she won't even pick up a woodcutters axe. Plenty of illusion, conjuration and alteration though. . . .

Solitude Guard's Armour

Light imperial braces, boots and occasionally helmet

Dragonbone bow, sword and dagger (although she seldom equips any of them)

Current Argonian character wears ebony set aside for helmet, I used shellbug helmet for my head gear. I occasionally switch to falmer hardened armor because it looks so epic. As for light armor, I usually go for dragonscale + some hood.

Due to the fact that dwarven armour looks so amazing, my guy is covered in it, apart from the helmet, which is an old Nordic one. Dwarven bracers of major smithing. Dwarven armour with arcane enchantment to boost heavy armour and dwarven boots of strength to take more load.

weapons I rely on an ebony bow with frost damage, an elven bow of fire damage and two ebony axes to trap souls.

I've still only been playing for a few months so my characters have run-of the mill stuff, but it works for them.

Birgitte: "The Do-Gooder" Breton Fire Mage/Enchantress/Jewelry maker, Lv 40-something
-Weapons: Incinerate, Fireball (for area damage), Thunderbolt (for magic users and pretty much anything on Solstheim). Exquisite Ebony War Axe w/Soul Trap enchantment (obvi - for Enchanting), Superior Ebony Fire Bow as backup.
-Armor: Stoneflesh spell, Lord Stone, Master Robes of Destruction, Fortify Destruction necklace & ring (silver and silver-ruby), Fortify Magicka Regen Silver Sapphire circlet, Nordic Carved boots (Fortify One-Handed for the one-shot soul trap), Nordic Carved gauntlets (Fortify Magicka just because). And it's Nordic Carved b/c it looks good with the blue-ish Master Robes, and b/c hubby Farkas wears the complete Nordic Carved set (w/Ebony Health Drain Mace and Ebony Fortify Block Shield), so they match.

Orandir: "The Opportunist" Bosmer Hunter/Smith, maybe Enchanter w/a little thievery on the side (I mean, if you're going to just leave your coin out there...), Lv 20
-Weapons: Superior-grade Dwarven Soul Trap bow w/Dwarven & Elven arrows for enemies, makes his own steel arrows for hunting (b/c why pay for that when you can make your own?), dual-wielding Skyforge steel daggers in a pinch. Uses occasional Fury, Fear and Conjure Familiar against groups and big baddies.
Armor: Superior-grade Leather, head to toe w/Fortify Archery, Health Regen, Carry Weight, and Resist Magic, and multiple Fortify [Sneak Skills] plain silver jewelry, all of his own craft (again, why pay for what you can make yourself?). He doesn't like clunky or bright armors, he's all about the camouflage. He travels w/Lydia who wears Superior-grade Steel Plate everything except for the No-Horns Steel Helmet and wields an Elven Battleaxe w/Fire Damage.

Scaled armour boots bracers, legendary smithed repeatedly. No helmet, circlet of fortify archery and Waterbreathing .
Glass bow of Fireshock normally or sometimes soul shock, eventually dragonbone version...Carrindor
Glass dagger of Frostshock......eventually dragonbone version called.... Serrindor
Plus a back up dagger of soul trap plus one other enchantment
Bracers have fortify archery and Carryweight
Boots have fire resist and Carryweight
Armour has fortify light armour and health
Special shield home made glass Haven of Fortitude rated 99 plus fortify block 47 and fortify health
Two vital home made apparels archers peace....a ring of resist shock 54 and fortify archery 47
And archers grace.......a necklace of fiortify archery 47 with fortify Carryweight 43

That's it in a nutshell

My character's armor ranges from nvde to daedric, and it all depends on what kind of character I'm playing. My current character is a thief, so she wears pants that make me think of spandex somehow... The pants (from the Hooters mod) are black, and skintight so they would make very little noise and have less chance of snagging on furniture or whatever. She also wears a very brief top from the hooters mod (but I retextured it for my own game).

The top has an enchantment, the pants do not, but she has special enchanted panties from the Osare Panty mod that boost her sneak. She has a couple of other pairs with various enchantments, but rarely wears those. She also has scaled boots and gauntlets with the gauntlets fortifying archery, but for nefarious purposes often wears the Thieves Guild boots. She has no helm, but wears various priest king masks to suit the occasion.

My characters are rarely lore-correct, and that suits me fine.

A combinationa of nightingale, ancient shrouded and shrouded armour. To that a cloak of health and a fur collar with some enchantment that I can't recall at the moment.

Nightingale blade, nightingale bow and the Shield of Solitude but when there is a special need I swap with crossbow, Chillrend, Dawnbreaker, Mace of Molag bal, Dragonbane and others. I should add extensive use of poison as well.

I created 5 characters and completed 5 full playthroughs of Skyrim totalling about 1000 hours.

2 x Pure Mages: Both wore robes and absolutely no armour or weapons.

2 x Battlemages: One wore Ebony armour (avatar) and one wore Stalhrim heavy armour. Both used matching swords double enchanted.

1 x Pure Warrior: Ebony armour and one handed Ebony Axe and Shield.

Magic robes with no weapons. Sneak, 1 handed, destruction, conjuration (weapons and raise dead), alteration (armour) and restoration (healing, blight, bonuses, etc, etc,) Might pick up a shield later, but usually manages without.

Heavy armor and great swords. Because i wanted a Spellsword who starts by nuking from orbit and then finishes enemies off in melee. Because i remembered how Arcane Warrior work in DA Origins

No crafting skills this time, since i found a wonderful mod that lets have smiths build stuff for me If only there was similar for alchemists and enchanters.