HI,
I been developing games in Unity for more than two years! You should first checkout the reviews I have got from my previous clients :)
I have gone through all your requirements. These services you would need for this game:
1. Photon Unity Networking: Multiplayer game and Chat
2. Playfab: Authentication, Admin control, player data/stats, leaderboard. Its complete backend service! Even you can send a news to your users. Easy to handle dashboard. FREE!
3. One Signal: Push notifications. FREE!!
Trust me, if you these are the best services available in this date! If you try another services you will surely end up with frustration! (had an experience earlier. I have developed more than 10 online multiplayer games under a same package)
Well, that was about the services you would need! Budget: The budget you are offering for this game is really low! Can you please contact me to have a discussion on this project, so we can discuss a budget too!
Thanks for your time :)