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Me and a few friends of mine decided to start playing 40K, we decided to make an unbound army to start with.

I already have (10x) necron warriors
130 pts
I then plan to add:
Anrakyr the traveler
160 pts

(5x)Lychguard
all hyperphase sword and dispersion shield
150 pts

(3x)canoptek scarabs
60 pts

Any advice on what I should get next to expand, or to change this list?

You should probably work on making it bound next.

A CAD (Combined Arms Detachment) only requires 2 Troops and 1 HQ so another pack of Warriors should do the trick.

Then you might want to work on filling a Decurion Detachment. That require taking a Reclemation Legion Formation which requires 1 Overlord (Anrakyr counts towards this), 2 Warrior units (you'll already have that), 1 Immortal unit (so that's your next purchase), 1 Tomb Blades unit (1 box to buy of this).

After that you'll need one of the Auxilary slots to complete the Decurion Detachment. This includes most of the other formation in the book or a unit of Flayed Ones or Deathmarks. Just pick what you like and throw it in there.

A Decurion Detachment is a great way to build a balanced list without really trying. Have fun!

Not sure if you're set on Anrakyr, but both Zahndrekh and Szeras are excellent starting options.

Stick with the Unbound as you grow, but yes you should work on getting your 2nd Troop soon. If they aren't getting their 2nd Troop, then don't rush to get yours.

After that you should lean toward Tomb Blades and Immortals. If you find you like those units, then try out the Decurion. Don't limit yourself to that if you want to try stuff out, and the fact that you're all starting Unbound is great as long as the plan is to end up with a Battle Forged list.

If you're set on using Anrakyr (not recommended), then a squad of Immortals would probably be better than another Warrior unit.

Personally, I'd just proxy Anrakyr as a generic Overlord and make a list that way.