Obviously, you weren't going to use rotten eggs, but I don't mean fresh as in not-rotten, I mean fresh as in recently from the chicken. Sure, fresh eggs tend to taste better and even have more nutrients, but that's not even the reason I'm pointing this out. The fact is that the fresher the eggs, the easier they are to poach. No kidding. Fresh eggs simply hold their shape better when slipped into the simmering poaching liquid.
If you happen to get your hands on some fresh pastured eggs - eggs from birds allowed to live in a field and scratch for much of their food, thus eating a varied and more natural diet - prepare yourself for some truly brilliant orange, verging on day-glo, yolks and wonderfully firm, bouncy whites. Learn more About Eggs here.
But, again, most importantly in terms of poaching, fresher and thus better quality eggs simply keep their shape easier when poached, so set yourself up for success and start with good eggs.
Note: Letting eggs come to room temperature before poaching them helps them cook more evenly. Take the eggs you want to poach out of the fridge at least 30 minutes before you plan to cook them.