I've written a FAQ to answer the question of how to handle fresh eggs from your backyard hens. The good news is that eggs from healthy backyard flocks have more natural defenses against bacteria than do supermarket eggs. But, storage in the fridge is still best. More here:
http://hencam.com/faq/handling-and-storing-eggs/
The other thing to know is that fresh eggs, when hard-cooked, don't peel easily! Save your eggs a week before you try. Here's a FAQ about that:
http://hencam.com/faq/hard-cooking-and-peeling-fresh-eggs/
Enjoy those delicious treasures from your hens!