Azure App Service plan

Free plan are good if you don’t care about backup, auto-scaling, staging slots and storage.

As of this writing, these are Azure App service plan;

For less demanding workloads (Dev / Test)

For most production workloads (Production)

Other production tier options are here;

To scale up/down, go to Azure web application and select Scale up (App Service plan). The selected pricing tier will have a blue border around it. Change the lower pricing tier based on your requirements.

Once you have reached to a point where you will need more than 1GB of storage and RAM, then I think S1 production plan might be your starting point. This offers 10GB of storage, and all benefits that free tier does not provide.

The cost of S1 tier is 73.00 USD/Month.

Reference

https://azure.microsoft.com/en-us/pricing/details/app-service/windows/

https://azure.microsoft.com/en-us/pricing/calculator/