This is just as much of a task as finding the right wedding day jewelry. I feel that choosing the right hair piece should be based on the type of dress you are wearing. Not all dresses look good with a 'birdcage veil', the same with wearing a fascinator. You don't want people to be distracted from the focal point (which is you) because you have over-accessorized.
Depending on your nationality, it may be necessary for you to have a more dramatic look. Culturally it's justified but if that doesn't apply to you then don't over do it.
For example Indian weddings are detailed and have many traditions. The brides are generally dressed in traditional garments, elaborate head pieces and henna tattoos. It's so beautiful. I've had the pleasure of styling hair for an Indian wedding, so I'm familiar with some of their traditions.
If your dress is more simple then you can accessorize a bit more. If your dress has more of a vintage feel to it, I love either the birdcage veil or the fascinator.
If you have alot of beading detail on your dress, then jewelry should be minimal. A cathedral veil will soften your look a bit. It gives a traditional feel to a more modern look. It's a great contrast.
Whatever head piece you are leaning towards make sure it compliments your dress.
It's a very important finishing touch to your look. It has to be Right.
I'm a stickler about dramatic earrings and necklaces paired together.