You did not specify whether it will be a Linux/Apache type site or Windows/IIS type. SQL Server implies Windows/IIS. You can use IIS in your local Windows. If you use Visual Studio then set up IIS before creating the web application in VS and then you can set up the web site to use IIS instead of VS's development server.
If this is a Windows/IIS type site then you can use Azure. I am not sure of your situation but it will cost little or nothing.
You have many choices for Linux/Apache type sites but IBM Bluemix has advanced technical capabilities and has at least a free trial period.
Bluemix and Azure both take time to learn but the advantage is that you have many more options than most other hosts. They support doing things the professional way.