At ArcGIS Pro 2.0 Favorites was introduced to manage connections to folders, databases and servers. This blog walks through how to effectively use Favorites. I think it does a good job providing examples of when you might want to add a connection to your Favorites versus when you might want to actually add a connection to all new projects. Knowing that there are these two options, and understanding the difference will help you manage your connections the most effectively.
As you get your Favorites set up and manage them, let us know where there is room for improvement. Specific ideas might already exist on ArcGIS Ideas. Make sure to look for what you want, up vote and comment if it already exists, or if it doesn't exist, add your idea detailing what capability would make your work easy in ArcGIS Pro.