RamyaRKS-7089, Bruce-SqlWork has shared some great insights and approaches on hosting the site with multiple options.
Since you have added azure-webapps tag, I'm just highlighting some additional hosting options from Azure standpoint.
Azure offers a number of ways to host your application code. The term compute refers to the hosting model for the computing resources that your application runs on. The flowchart in doc, will help you to choose a compute service for your application.
This article helps you understand the options and make the right choice for your web application.
Azure offers a number of ways to host your application code. The term compute refers to the hosting model for the computing resources that your application runs.
Long answer: Just to provide you a good understanding on hosting website on Azure. Azure offers several ways to host websites: Azure App Service WebApps (PAAS solution), Virtual Machines (IAAS), Service Fabric and Cloud Services. You can leverage the service that best suits your requirement.
I suggest you take a look at the criteria and flow chart (Decision tree for Azure compute services), weigh the platform strengths based on your organizational requirement and then chose the best platform.