Hello @ChrisFig ,
Azure has wide range of marketplace images with both Windows/Linux OS and also azure supports "Bring your own Linux(BYOL)", some customized/generalized images under non market place.
You could configure a VM just like the one you had on-premises with azure market place images as per quick-create-portal. You can check Azure endorsed Linux distros from below link and create the VM with OS that is compatibility with your application.
Reference: endorsed-distros
Chosing the storage depends on the VM utilization. Typically you would chose whether you want to use premium storage or standard, for details refer to premium-storage-performance
I would recommended to check Azure Media Service based on your scenario, For quick starts for encoding and streaming and see if you get better performance for your scenario. https://learn.microsoft.com/en-us/azure/media-services/latest/
Blob Storage: Stores large amounts of unstructured data, such as text or binary data, that can be accessed from anywhere in the world via HTTP or HTTPS. You can use Blob storage to expose data publicly to the world, or to store application data privately.
Azure Media Services Encoder: Encoding jobs are one of the most common processing operations in Media Services. You create encoding jobs to convert media files from one encoding to another.
Azure Media Services Streaming Endpoint: A streaming service that can deliver content directly to a client player application, or to a content delivery network (CDN) for further distribution.
Media Services supports integration with Azure CDN (for more information, see How to Manage Streaming Endpoints in a Media Services Account). You can use Live streaming with CDN. Azure Media Services provides Smooth Streaming, HLS and MPEG-DASH outputs. All these formats use HTTP for transferring data and get benefits of HTTP caching. In live streaming actual video/audio data is divided to fragments and this individual fragments get cached in CDN. Only data needs to be refreshed is the manifest data. CDN periodically refreshes manifest data.
If you have plans to stream to possible multiple users consider to use Azure Media Services and also CDN to save cost with network out:
The output from Media Services is a blob into a container.
For more information refer to this article: https://learn.microsoft.com/en-us/azure/architecture/solution-ideas/articles/digital-media-video
Please "Accept as Answer" and Upvote if any of above helped so that, it can help others in community looking for remediation for the similar issues.