Developer for Salesforce and Mojo API Sync(Read and understand ->Bid)

We currently have PropertyBase (Salesforce) where our Contacts are stored, and are using Mojo Dialer (https://www.mojosells.com/) for an automated dialer. We have tried to use Zapier to send information between Salesforce and Mojo, but have found it too difficult to customize (it currently can’t send field updates from Salesforce to Mojo because it does not know their unique ID and we have no way of exporting it from Mojo) so we have decided to try to build something custom.

We want to have a two-way data sync between Mojo Dialer and Salesforce contacts.
• All Salesforce Contacts will be sent to Mojo, but not all Mojo Contacts sent to Salesforce (manually triggered when they meet a certain criteria).
• Match based on Phone (or Email if blank).
• The sync should run hourly (or more frequently if possible) to keep data updates between the two systems passing back and forth.
• Salesforce currently has 8,400 contacts (average number of new contacts created per calendar month: 350)
• Mojo currently has about 20,000 contacts
• We have a list of about 10-15 standard/custom fields that we would like to pass back and forth between Salesforce and Mojo if they are updated on either side