Storing the ice cream: I put an empty Pullman Loaf Pan in the freezer, so it would be cold when I put the ice cream in it. Freeze until ready to serve. The pullman pan comes with a lid, so it is a great way to store the ice cream. I always place parchment or plastic directly on the ice cream so it won't get freezer burn. As if it would last long enough to get freezer burn.
Serving the ice cream: This seems like a silly tip, but how you serve the ice cream will make a big difference. If you can serve it within an hour of churning it, that is ideal. But, that isn't always possible. If you remove the ice cream from the freezer and it is very hard, you'll want to let it sit for up to 10 minutes or longer for super dense ice cream. This will "temper" the ice cream and put it at a nice consistency for scooping and eating. If it is too cold it won't scoop nicely and you won't taste the subtle flavors.