Thinking about appearance.
Visually they should be immediately identifiable as their species, with an emphasis on being both distinctive and easily cast as a compelling character. That might mean being badass, sexy, cute, intimidating, or whatever other attribute the player wants to focus on.
I agree with turning them into somewhat luminous beings. Perhaps having them be translucent or having a high sheen to them.
Apearancewise, they should be allowed a ton of variation. Bronze statue people, animal headed people with feathered/furred arms and legs, multi eyed eldritch horrors, christian angel people, and 'human but a bit sparkly' should all be supported.
Current Aasimar lore clearly includes non-human traits that are identifiable as such - Metallic freckles, luminous eyes, a shadow that's a different color, a halo, rainbow-gleaming skin.
Probably, the luminous aura is what all Aasimar share in common, for the sake of the IP recognizability. Then individuals might be translucent, metallic, or so on. Brainstorming, maybe the luminosity can be a distinctive light show, like two colors of light shifting back and forth? Maybe runes of light form within the aura? Actually, I strongly associate the Astral Plane with thought, paradigm, symbols, language, and meaningfulness. Let the aura of light form words in calligraphic letters of light within it. So, whenever one sees a character with an aura and words within, it evidences an Aasimar.
The Aasimar form look like anything. Pick any creature in the Celestial planes for inspiration. There can be Celestine (?) (Mount Celestia) who looks like an Elf, Eladrin with an animal head, or unicorn, orb of light, whatever the player conceives. Perhaps the only limitation is anthropomorphic Humanoid, including Human.
The two defining features of an angelic being are their wings and their radiance-affinity magic (sometimes manifesting as a halo). The former isn't usually the focus in favor of the latter, but why not? Its something different, widely applicable to many classes, and can be eeasily implemented with so many examples to draw from.
I have mixed feelings about wings. Some concepts definitely. Other concepts definitely not.
Also, I'd personally want to avoid making them just radiance tieflings insteead of fire, necrotic and poison tieflings.
Heh, speaking of which, in parallel to the Tiefling of Fire, Necrotic, or Poison:
For Aasimar, Radiance, Psychic, and Force.
Radiant for Lawful Good, because Solar.
Psychic for Chaotic Good, because Fey.
I guess that leaves Force for Neutral Good, maybe because creation.