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Hi, as the title states this is my first army as I am new to WH40K.

HQ:
Autarch - Fusion Gun, Mandiblasters, Spear of Teuthlas, Warp jump generator (120)

Troops:
Guardian Defenders x10 (90)
Heavy Weapons Platform - Starcannon (20)
Wave Serpent - Shuriken Cannon, Twin-linked Eldar missile launchers (140)

Rangers x5 (60)

Fast Attack:
Vyper - Brightlance, Shuriken Cannon (70)

So, have I at least got it almost right

Autarchs cannot take the Spear, only Psykers can.

I would change your wave serpent layout to:
Wave Serpent,scatter laser,holofields,shuriken cannon-145
it's only 5 points more, but the laser twin-links your other weapons.Also as a whole this tank pumps out 7 str 6 shots and d6+1 str 7 shots, way more effective than missile launcher.
Other than that, your list seems alright.I prefer running my autarch with a mantle of the laughing god, on a jetbike.This grants him toughness 4 and a 2+ cover save.
My list would look like this...
Autarch,jetbike,mantle,fusion gun,laser lance,banshee mask,mandiblasters-160
Wave Serpent,scatter laser,holofields,shuriken cannon-145
5x Dire Avengers-65
3x Windrider jetbikes,shuriken cannon-61
Vyper,bright lance,shuriken cannon-70
501

Listen boy, this is the one first peice of eldar advise that you need to remember.

-the most/best/only way to competitivly run wave serpents is with scatter lasers, and when you do this, it makes them one of the best units in the game,and the best in the codex.

You might to want to consider getting some warp spiders. If only for their sheer awsomeness

Thanks for the tips.

I realise now that I should have specified this army is not only my first, but also what I listed is all I have, so any changes can only made using the listed units.

I made some changes and it now looks like this:

HQ:
Autarch - Fusion Gun, Banshee mask, Jetbike (100)

Troops:
Guardian Defenders x10 (90)
Heavy Weapons Platform - Starcannon (20)
Wave Serpent - Shuriken Cannon, Twin-linked Scatter Lasers, Holo-fields (145)

Rangers x5 (60)

Fast Attack:
Vyper - Brightlance, Holo-fields, Shuriken Cannon (85)

(500)

there you go. thats a good list. only problem, i see is where is the autarch going? i dont see any unit ofr him to hide in. find points for mantle of the laughing god for him, and laugh when the enemies shots do absolutly nothing to you