Just to point out Sam. If you want to host ColdFusion I would go with AWS. With Azure you WILL PAY more money with drastically less control over your IPs, routing, DNS, and other needs. In addition you have less control over your OS in Azure. I'm a bit fan of Azure, but if you're not pretty much 100% .NET stack it isn't the greatest idea.
Going with AWS (and possibly some of the other options) gives you much more control (directly to the image) at about 2/3rd the cost. The more instances you need, the more time you know you'll need them, you can get reserved instances which are a 1/3rd of Azure's instance cost.
As for the storage, any instance is volatile, meaning you'll need to use managed storage or the distributed relational database options such as AWS's RDS or Microsoft's SQL Azure. Either solution is good, depending on the amount of storage space and compute power you'll need for the ColdFusion Service.
If you have .NET Applications that you're concerned with, sitting on ColdFusion or something, and you want to do Azure Deployments (i.e. to a Web Role or directly to a Services Role) then you may want to use Azure. But I doubt you'll get a good price point trying to configure ColdFusion for use on/in Azure.
My quick advice, either:
A. Stop using ColdFusion and migrate to another solution and move into Azure with a more cost conscious architectural option (i.e. a more SQL Azure + ASP.NET oriented solution) or
B. Use AWS and host the solution as is with ColdFusion.