What is your "Main" interface for Groups?

yes more and more apps are built on Office 365 Groups. 

The easiest is to present groups in Outlook as a natural evolution of DLs with history and context, no need to change tools/UI.

Another way is to introduce it based on use cases, here is an extract from the Microsoft Teams documentation: https://www.successwithteams.com/ (more content on FastTrack as well)

Microsoft Teams:

• Leveraged by users and teams who are looking to collaborate in real-time with the same group of people.
• Helps teams looking to iterate quickly on a project while sharing files and collaborating on shared deliverables.
• Allows Users looking to connect a wide range of tools into their workspace (such as Planner, Power BI, GitHub, etc.).

Outlook:

• Leveraged by users looking to communicate in more formal, structured manner.
• Provides specific business processes that require email usage to transmit documents and information inside and outside corporate boundaries.
• Communicates and connects with users who are outside of immediate workgroups or organizations.
• Has low-frequency interactions that do not require immediate action.

Yammer:

• Leveraged to help connect users across the organization share best practices or participate in a community of practice.
• Connects one to many and crowdsource ideas and topics, through its enterprise social network.
• Helps customers looking to foster two-way conversations between leadership and staff.
• Supports communities for company services.

Skype for Business:

• Allows organizations with real-time communication and collaboration both internally and externally with customers/partners.
• Provides meetings with audio, video and content with small or large teams (including Town Halls with up to 10,000 participants).