ACI current pricing as of Dec 2017
1 create request x 1GB memory x 1 month (2592000 seconds) x $0.0000125 (GB/sec) = $32
1 create request x 1 CPU Core x 1 month (2592000 seconds) x $0.0000125 (GB/sec) = $32
Total ~ $64 / month.
I think you might be better off running an Ubuntu VM with Docker for your services and then add Azure Databases for MySQL for persistence. That is how I deploy inside azure.
