Thanks everyone for your opinion on the matter, I think everyone here has suggested important features that could indeed improve the experience of a ranger playthrough.
As already mentioned, I agree with the fact of choosing one specific animal once we reach level 3, and I agree also with the fact of being able to choose his physical traits, something like size, fur color any particular mark, something that affects only the aesthetic part of your companion.
Alongside this an origin option could be added, maybe something along this line:
"Kula" is now your closest companion, a strong bond between you two has grown, he is ready to follow you and have your back at all time no matter the cost, so do you.
Trust and mutual care enforces this bond every day, but tell us, how did you two meet in the first place?
Saved "him or her" from a group of hunters. (+ 2 constitution)
Found "him or her" lost in the outskirts of a city. (+2 Dexterity)
Followed "his or her" bloodtrail, after an exausting fight with another animal and cared for "him or her". (+2 strength)
I know it doesn't have to be exactly like this but I feel this can really create some affection from the player towards his furry companion.
I also like the idea of needing to revive our friend via scroll, but if this is going to be implemented, than they definitely need to buff his stats since with the current shallow health pool they get you will need dozens of scrolls...
I also like the idea of a hound, of something closer to a human rather than a wild beast, of course I would not like to rule out the chance of having a bear though.