We have just applied as residents under the 'Self Sufficient' cathegory. We are EU / EAA nationals but they still require quite a lot of information.

Comprehensive health insurance covering us and our children
Proof that you have money in the bank (not sure how much, have heard 20.000 Euros) or income from other sources, at least 1600 Euros per month to cover family of four (I was amazed at this low amount as there's no way we could live on that amount here!).
Rental agreement or proof that you own property here
Marriage certificate
Children's birth certificate.

There may be other documents, I can't remember right now. You need originals and copies of everything.

Good luck!