1) Express gratitude and enthusiasm. If it's your first choice, let them know! Tell them why you want to join.
2) Describe your value. Bring up your background again and refer to the points they brought up during the process as to why they like you. Then list two or three more reasons why you'd be a good fit.
3) Explain your situation and describe your needs. Ask for permission to address a few things about the offer, then breakdown your living or commute situation. Talk candidly about what you're targeting in order to support yourself and your family.
4) Ask for feedback. Remember, you're talking to your potential boss. Open it up to them and let them know that you value their opinion.
Be genuine and honest. You don't have to play hardball to get the offer you're hoping for.