We'd like to have all available issues type be the default when creating a new next-gen project? Is these a place to configure that or an you only add additional types once the project is created?
At present each Next-Gen project comes with a standard set of issue types (set at creation or suggested when configuring the project). If you have custom issue types, you'll need to add them to each project post-creation.
The roadmap does confirm that configuration sharing is coming in 2020:
For teams that want to share next-gen project configurations and best practices, you’ll be able to copy a project, including custom issue types and workflows. Projects will continue to remain independent after you copy them. This will be particularly helpful for teams that want to share next-gen best practices across teams.
See it and other upcoming releases on the roadmap here.