We need to set up a sync process between Salesforce and our Dental Practice Software.

General information for the business: We run multiple dentist practices with a head office administration where all management, sales and marketing is handled.
Description of requirements/functionality: We are looking for someone familiar with the Salesforce API and has some experience with it. The dental software uses REST.
The API supports Cross Origin Resource Sharing (CORS) for AJAX requests from any origin. JSON will be returned from all responses from the API, including errors. Their API features are all pretty well documented in the developer area of their website. It works on the cloud as does Salesforce.

The client record, appointment record, calendar, accounts and notes areas will all need synching to Salesforce from the dental application and back the other way too.
Specific technologies required: Salesforce API, REST, API development
Extra notes: Please quote a fixed amount for the job to be complete and functional, along with how long it will take.