Undoubtedly my all-time favorite Osaka moment is when she makes her big appearance for the first time at about :50 seconds in the above video.
This was the very moment that I fell deeply, and eternally, in love with Osaka. When I witnessed my dear and beloved Ayumu stride serenely into the class-room, I had to take a double-breath in pure amazement, and I felt a warm tugging in my heart...
The heavenly rays shining down upon her, the ethereal chimes, her dainty ivory-socked feet with cute little ankles poking subtly out, those particularly defined thighs composed of the finest flesh leading up to her fair and maddening loins, more meticulously drawn in this one shot so as to impact the viewer even more so than any other scene.
If Azuma (or whoever animated this scene) was going all-out in order to cement Osaka as the best and most beautiful Azumanga girl of them all, then I'd say they succeeded, because Osaka had me in her clutches from the get-go.
Sorry for the tl;dr wall of text. I am a bit of a poet (or at least I am in my mind) and I feel good expressing my affection for Osaka through the written word.
Here's another Osaka vid, this one made by a fan from the 2005 Anime Music Video (amv) called "AMV Hell 3."