Wordpress + REST API client

We want to implement a Deal-finder web application allowing users to find good deals on hotels and similar.
The application will be based on WordPress and will consist of the following:
- Landing page with access to "Login" and "Request Invitation" popups
- Search page with 7-8 fields (location, number of adults+children, dates of travel etc)
- The search will be carried out via a REST API call to another server
- Results page will show a table with rows for each room option and columns for different prices (The API response (JSON) will contain all data needed to populate the results page)
- User can click on links in the table to see a popup with more info and then to navigate to an external / 3rd party site

We will provide input from a web designer indicating which WordPress theme to use and how each page is to be laid out.

We will provide complete documentation for the API.