At the moment, the People API does not retrieve all the contacts that the Contacts API did, but is suggested as a replacement. If I wanted the old list that included Most Contacted and Other Contacts, I believe I would need the Contacts API. How long is this API intended to be supported?
Yes, People API will replace the Contacts API.
The new People API uses the newest protocols and technologies and will eventually replace the Contacts API which uses the GData protocol.
The Contacts API has not been deprecated yet so we don't know how long it will be around. Once Google deprecates an API it is typically available for 1-3 years before being fully shut down.