I watch a lot of Food network, and they always say not to use fresh eggs for boiling - something about as the egg ages it loses its water and the air bubble grows? But instead of a few days, I think they said 5-7 days.
This link most resembles how I do my eggs and I rarely have troubles with sticky shells or green yolks:
http://www.wikihow.com/Boil-Eggs
I usually just dump out the boiling water, cover the eggs with crushed ice (since my fridge makes it) and cubes and leave them be til mostly melted. When peeling, I put down a tea towel, gently crack the fat end and slowly roll the egg around until it has little cracks all over, then I finish peeling under water - letting water get between shell and egg helps.
BTW, when I worked at Kohl's, I was able to get one of those "as seen on tv" egg peelers - you know, the kind that looks like a manual air pump?- for $0.50. I couldn't resist trying it, just for laughs. My dh and I had a blast shooting eggs all around the kitchen with that thing!
It actually worked about 1 out of every 3-4 tries, but it was always fun! Oh, I wish I could give you a visual on that one...whooosh--plop-splat!