The only rule about what spirits look like when manifesting is that they are obviously not-human... so a fire spirit might manifest as an avenging angel, but there is no way that anyone would confuse it for a human. There is a critter power for that called realistic form that provides that level of subtlety, but most spirits don't have it.
Since it is mostly cosmetic, I let the PCs decide that it looks like, but as a side note, it is 'assumed' that manifested spirits are also about the size of a human, with invoked spirits being larger.
Which reminds me of a story from 3rd ed, when it was easy to summon multiple watcher spirits and watcher spirits could manifest, even if they were insubstantial...
So the team I'm on needs to get into a locked facility... it's guarded but not locked down. So if we can get past the two guards at the loading dock, we're good. We can see the guards with visual magnification so seeing what they look like it's a problem. I summon three watcher spirits. The first two, I summon to look like pale, whispy versions of the two guards from the torso up... the third as the Grim Reaper... I order the two 'guard' watchers to float over in the astral only and stay near their respective guards but do not touch them. They are only to manifest when they are touched by the third, then they are to scream and float away while manifested... the 'grim reaper' is to manifest 20m from the guards, rush in and swing once at each spirit and then float away...
The guards see the grim reaper coming... it strikes each of the watcher spirits, which is really close to each guard... the guards each see their 'soul' be struck down and float away with the grim reaper... They panic and run away, leaving the loading dock free and clear...