I’m about to get started converting a C# based desktop app to be web based. For a couple of reasons, I would like to cut the GUI from the logic via a web service. Microsoft has asmx files, WCF, and probably something new at PDC next week. Data can be passed via SOAP, REST, JSON, and probably 12 other ways as well.
Could anyone suggest the .NET framework I should get started with?
You are about to move to a new platform. I would go for WCF. It can support all your needs.
Initially when you move you can use httpBinding and that is very close to ASMX web services and is based on SOAP. If you later require some advanced features, then you can definitely utilise webHttpBinding and that will give you REST and JSON based interface. WCF is very powerful programming model and you should definitely move to it.