Architectural Question: Web Application + RESTful Web Services

[eluser]CodeIgniterNewbie[/eluser]
We are going to start working on a web app and would like to expose an API to it using REST. Is it a good idea to create the API first, then have the web app use the API for its functionality. This way, the exposed API is exactly the same as what the web app is actually using.

Additionally, there will be 2 teams working on the entire system: one for the web app, the other for the API. What's a good way to split development in such a way that Team A is not aware of Team B's code -- and vice versa? Do we use different servers and different SVN projects? Something else?