If your eggs are for your own consumption, and you simply want to eat as organically as possible, don't worry too much about things. If you're seling them as organic, you need to research it and make sure you do everything right. Only 100% organic feed from day one is just the tip of the iceberg.
Fence-wise, I think it really varies on the breed, and even individual chicken. My girls respect even really low fences, like 2 or 3 feet, because they have plenty to keep them busy in the yard. But I do supervise them. I'm sure that at some point, if they were out dawn-dusk, one of them would get out.
Is your concern that they'd ingest something non-organic on the neighbor's property, or that they'd bother the neighbors? I'm a little confused about the 2 questions...
Breed-wise, the heavier and more domesticated breeds (ie barred rocks, buff orps, cochins?) are probably less likely to go roaming than the "wilder" breeds. Look up the breeds and the ones that say they don't stand confinement as well and are best on free range, those are the ones I'd think would probably range a lot further. My heritage breed girls tend to be homebodies!
