Congratulations on your new role!
I've been training Communication Skills within organizations for 20 years. I've got some great free resources at my site conveyclearly.
Most of it is about being confident, persuasive, authoritative, yet warm!
My first tips for you as a new manager are to:
1. Use an authoritative yet warm voice. To get this voice you have to be relaxed, use lots of air for your speech, make sure you go down at the end of all declarative statements.
2. Paraphrase what people say. Miscommunication can lead to bad blood at the workplace. Make sure you clarify that you heard your colleagues correctly. Also, it makes them feel validated which is great for a positive workplace experience.
There's lots of stuff on my blog & website that helps you to communicate better with your staff, boss & clients. I've got a free download on the site called 9 Secret Steps to Influencing Others.
I hope it helps! You can contact me with specific questions anytime!