another +1 for Three 44's.
Having your eye centered behind the peep is critical. This in turn requires the correct cheek weld to the stock to be consistent (very important). Having the butt in your shoulder, or cheek on the stock (the latter is dependent on the former), in a different place from shot to shot will mess up your sight alignment. Consistent correctness in these contacts is important.
Having the peephole too small can be troublesome. A small hole helps center the eye better than a large one, but a small hole reduces both the light available to the eye and the total field of view. Once you get your consistent correct cheek weld down you don't need the small hole for precision, and the bigger hole lets you see the whole world through the peep, even in dim light.
A really large peephole rear aperture with a thin rim is called a ghost ring. The rim seems to disappear when the front sight is sharply focused on by the eye. It is extremely fast, almost like a bead on a shotgun, and gives the most light transmission, but is still precise enough for 'normal' usage.
Front sights are another story. I always replace a bead front sight with a post, since the square top of a post gives a much better and more precise aiming index than a round bead does, especially for long shots on small targets. On a bear or hog at bad-breath distances, it's not an issue.
Aperture sights are great when you get to know them. If you can see your target with your naked eye you can clobber it. The one-MOA elevation/windage clicks on an M1 or M1A/M14 will sure spoil you.