Long Range: Daedric Bow of Blaze

Short Range: (Call me a hypocrite) Blades Sword and Dragonplate Shield

Long range: Ebony bow enchanted with absorb health/Nightingale bow

Short range: Two ebony swords, one enchanted with fire and the other enchanted with frost

Long range: Auriel's Bow

short range: Dragonbone Sword(never tried it)

but wait a second...it's made by my own bones!

Oh I forgot short range, Dawnbreaker

Long range: Dragon's Breath (Dragonbone bow with both fire and frost damage enchantments)

Short range: Dragon's Tongue (Dragonbone greatsword with similar enchantments)

(These are not unique weapons, but instead they have a custom name, for those of you who didn't know.)

Early on I got lucky and picked up a Dragonbone sword as random loot somewhere, and used the crap out of it. That thing is awesome.

Later in the game I went and smithed a Dragon warhammer and gave it both fire and ice enchantments. Damage output is insane.

Edit: Also have a stalhrim bow, which I use sometimes, but I'm bad at archery so the effect is kind of lost for me.

edit 2 Okay Dragonbane is not "random loot," not sure where I got that idea from. I'm good at this game.

im an archer 

Dragonbone Bow for range, Dragonbone Sword and Spellbreaker for melee. Both enchanted with fire and absorb life.

Ahmuldein
The Staff of Gjins Glunderson I think is how you spell it. If you have the soul gems for it your good to go

Staff of Jiriik Gauldurson is the correct spelling. Almost had it.

Volendrung is the best, it can do the most damage out of all the weapons (just heard this). My favorite skill tree is two-handed and I like hammers the best slow but do loads of damage.

Hmm, in my more recent playthrough I've been doing a LOT of dual-weilding doubly enchanted swords. Burn, drain health, soul trap and a few other effects, all in one. Combine with sneak attacks, and draugr deathlords are falling in one hit :D

sword

I tend to gravitate to swords. My favorite has been Dawnbreaker and katana variety.

My favorite shield so far is the stahlrim shield.

For long range, I prefer bows over crossbows. My favorite bow is Auriel's bow with eleven arrows. (I found eleven to be a good balance  between effiecent and abundant.)