I'm currently working on an unaligned human psycher and debating my power choices.

I'm most interested in the Divination Powers currently, with a dash of Telekinesis, and once I start pulling in XP I'll continue in the vein along with Exalted powers and Biomancy powers to round everything out.

How well do the Divination powers work? Any suggestions?

-edit-

This is what I'm currently considering, my Psy Rating is 3, for reference (4 with Child of the Warp)

Divination Powers: Precognition, Precognitive Dodge, Precognitive Strike
Telekinesis Powers: Mind Over Matter, Telekinetic Weapon

Characteristics: WS 49, BS 25, S 25, T 35, Ag 35, Int 50, Per 50, WP 50, Fel 20, Inf ??

My Plan: Walk around with a Manifested TK Weapon, using Precognitive Dodge and Precognitive Strike to Evade and Attack. Eventually I want to pick up the Warptime and Telekinetic Shield Powers as well.

Unknowns: I am a complete 40k newb, and have never RP'ed in the 40k universe. I dont know if what Im trying to do is feasible, is it silly to pit a human psyker with these powers against astartes and the like? How badly will I get smashed to bits?

First of all, that statline seems very point-buyish. If so you should really have atleast 40 toughness (as it seems survivability is an issue for you, and higher toughness is needed for some biomancy powers if that was the plan). Seems strange that your GM would allow you to min-max to that extent (having 3, almost 4) "primary" stats maxed out and nonexistant BS, S and Fel.

Drop telekinetic weapon, or atleast don't use it as a main weapon if you really want to be as effective as you can be. You have access to force weapons, which are soooo much better - check the "Force" special weapon trait and you'll understand why *hint* channel killing will *hint*.

You probably want to pick up atleast swift attack aswell.

You PR isn't actually 4 with child of the warp, you only add +1 when you push (on top of the other up to +4, so you could get +5 in total that is).

How you will fare? Of course you won't be as tough as an astartes due to no power armour or unnatural toughness, however you can get your hand on better armour and, this one could be important, pick up the nurgle power which grants unnatural toughness. After that you would probably fare better.