Do not apply for a (a)(6) EAD!! If you do apply for it, then it will be a futile attempt.
After marriage, file I-485, I-131, and I-765. The (c)(9) EAD and AP applications will be free if full I-485 fee is paid: https://www.uscis.gov/i-485
Filing Forms I-765 and I-131 with Form I-485
If you submit Form I-485 and pay the required fee, you do not have to pay an additional fee to also file Form I-765, Application for Employment Authorization, and/or Form I-131, Application for Travel Document, for advance parole. You may submit these forms together. If you choose not to file Form I-765 and/or Form I-131 with your Form I-485, then you must submit a copy of your I-797C, Notice of Action, (also known as your receipt) as evidence that you filed Form I-485.