i haven't made a study of alien species, yet i'm familiar with the topic.
grey aliens are perhaps the most commonly reported variety involving "encounters".
the current thinking, that i'm aware of, involves the idea that there are
a 'family' of species inhabiting various portions of space. the greys,
although quite often experienced as being indifferent, or even hostile
to humans, are thought to be the most advanced of this family (at least
in a technological sense). the species most like humans are said to be
pleiadians. there are also arcturians, and four(?) other species in the family.
the greys are usually described as being short in stature, though there are
said to be a taller version as well. i think the Betty and Barney Hill abduction
is thought to involve greys:
https://en.wikipedia.org/wiki/Barney_and_Betty_Hill
it might be better to begin exploring about the pleiadians first.
Bringers Of The Dawn
https://www.youtube.com/watch?v=TZr1ucX7pkY
for some reason, the dream you'd described had me thinking of something
'babylonian' looking. like the statue of nabu 'come to life'.
https://en.wikipedia.org/wiki/Nabu
which lead me to the thinking of the elohim, rather than the greys.