AP application is easy and you don't need to spend $305 for that.
In hard way I learned that it's better to provide them EVERY POSSIBLE docs that you think they CAN ask for. Last year when I applied for my wife they generated RFE for MY I40 approval (I have provided my GC copy with application, why do they need my I140 approval notice for my wife's AP application?).
Anyway, this year I decided to not to be logical. I provided following documents an this she got approval within two weeks.
This year I provided following docs:
1. I131 application form
2. a letter specifying why you need AP (just specify that you are planning to travel this year).
3. check for application ($110)
4. copy of passport
5. copy of I94 (both sides)
6. 2 ADIT style photos
7. copy of previous AP (if any)
8. I485 application receipt
9. I140 approval (or application) receipt
10. copy of marriage ceritificate
11. copy of my green card.
12. copy of my I-485 approval
13. copy of my passport
You don't need items # 10, 11, 12, 13 if you are primary applicant.
I sent to application to same post box for I485 application (PO box 10485) - specifying "Application for I-131 (Advance Parole)" on envelope. Last year when called USCIS, they asked me to send to this post box. But I saw in this forum people sent to other general post box and got approved.