Which species would fit best?

I'm using a dark matter Blob for mine. I've found it's a lot more diverse of the pets. Although the experiment and Rift pets are pretty good too. the ghost seems like it would make a great possessive spirit.
Those are just my takes tho. ^_^

Kind of depends on which direction you're going with.

1. i.e. shapeshifting abilities but with an actual base form, in which case I like the common experiment , and the - common experiment - -

2. If you're going the way of say, something similar to Odo from Star Trek Deep Space Nine where when they're not shapeshifting have no actual identifiable form. Odo from Star Trek when not in his human form was primarily an amorphous blob with no identifiable form then,

a) blob pet or rift pets work really well for something like that.