Sounds like an interesting project...
You can host WCF Services in a WCF Service Web Role, which is a web role with starting artifacts for hosting WCF services.
For entensive processing you can use worker roles. When data is received, a WCF service cam place a message on a Service Bus queue, which will be received by a worker role, which can process the data asynchronouslty.
For data storage you could look at the Table and Blob storage in Windows Azure Storage, or look at Windows Azure SQL Database if you need relational storage. There are advantages and disadvanteges to both approaches.
There is quite a lot of technology to evaluate, so it might be worth running through a few tutorials to get an idea of what will make for the best implementation. The Windows Azure Training Kit is a good starting place for this.
http://www.microsoft.com/en-us/download/details.aspx?id=8396
Regards,
Alan