You need to show the basis of your AP usually your I-485 receipt if you got your AP because you are an Adjustment of status applicant. In addition, it is wise to carry your paystubs if your employer is your GC petitioner to prove that you are still employed with the same employer. Also carry previous H1B receipts if you have them assuming you had an H1B in the past.
Remember that if you have accrued illegal presence in US (more than 180 days is the period I think), you will be subject to the 3-10 bar
Hope you have a safe trip!
regards,