If you are specifically targeting the web stack, ASP.NET MVC + WebApi would be the right combination on the server side.
The inherent support for JSON on both client and server makes a JSON-based API very popular. More and more public APIs from most of the providers are JSON-based or at least support JSON.
WCF may have its applicability in terms of server-to-server communications but for a web stack, I don't think it's a good fit. If you have a requirement to support multiple transport mediums, bind with protocols other than HTTP, support binary serialization for performance, complex security requirements, then WCF can help you.
Also for JSON based API, I suggest you use WebApi instead of using MVC and returning a JsonResult
.