Congratulations. I got also my first job offer 6 months ago, don't be scared. It may be nervous the first week. But just act normal and don't be shy. Engage in convcerstaions, be social. It will help with the stutter. And don't be afriad to ask queations beacuse of your stutter. It will make it worse. What have helped me is i prepare my queations if it's a really really big one and important.