I would most certainly pick up Burdhur, in my opinion he is one of the most valuable pieces available to Angmar. If you are going to get spectres then go ahead, but make sure that you spread them across your army, placing only 1 or 2 in each warband as opposed to making a warband out of them.
To start out with, only bother with either the shade or the barrow wights, you won't need both to begin with. Make sure to mount the witch king on something, and perhaps pick up a box or two of warg riders, because:
A: Mounted support for the Witch-King will help.
B: Variety is the spice of DEATH!
Now for some tips on magic (incase you are new to the game)
If you're gonna field the WK at lower than full power, then make sure he has 3 might.
Generally just keep him out of combat and target big heroes. If you feel like you have alot of will, don't be afraid to cast a drain courage every now and then, even if the enemy isn't broken, alot of players don't see the value of courage and might not even bother resisting it. Also now that transfix is a bit weaker, and every hero can raise their fight value with heroic strike, you probably won't be casting it a whole bunch. Black darting horses is also a very effective technique against enemy heroes. I'd generally shy away from channeling any spells, save your might for heroics 
However the main thing to do with the witch king is 'your staff is broken'. If your enemy is fielding a wizard then go all out to ensure you break their staff early on.
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