It doesn't seem to matter for me, old, new, sometimes they are super easy to peel, and sometimes not. I always cook hard boiled eggs in softly boiling/simmering water, especially for Easter eggs. If peeling imediately, I empty the water from the pot, and shake the eggs around to craze the egg shell, then run under cold tap eater until cool enough to handle. This method works well for me most of the time
However, there are times when the shell just sticks, even when I get part of the skin to come away from the solid egg white. As far as uses for the egg in no prefered order:
1. Egg sald for sandwiches
2.Sliced, or quartered for potato salad
3. Sliced to add to various leafy salads
4. Pickled eggs
5. Crushed, and placed on buttered toast
6. Sliced and added to soups
7. Eaten cold with salt and pepper
8. Added to breakfast buritoes
9. Sliced and added to ramen
10. Chopped into ham salad
Chopped and added to corned beef hash
11. Deviled eggs
That's some of the eays I use them.
Seeeeya; Chief Longwind of the North