I think this should be fairly easy, I work on similar project at work, but I have a few questions, so please send me a message if you are interested in my offer.
Here goes the questions:
1) Do you have azure subscription already or you need to create one?
2) To connect to Azure SQL database, you need to allow the IP address you are connecting from and I have no experience with costPoint, but if you can provide the IP adress, the communication can the be done on standart 1433 MS SQL port.
3) You really should use SendGrid when sending emails in Azure, it has really simple implementation, have you considered this?
4) How do you plan to run your code in azure - in a website, or maybe a cloud service..?