A Homunculus is defined in ROP:F as a faerie with some rather specific requirements which grants its caretaker a variation on The gift which is both gentle and associated with faerie, and has a number of drawbacks (like nobody else can look at the Homunculus or it dies and there goes your Gift), so probably not a familiar...
That's why I said some kind of 
Any small, vaguely human-like creature would be perceived as such.
Realms of Power: Magic also defines homunculi. Or rather, it defines Mandrake as a thing that can be turned into a type of homunculus and bound as a familiar. They're associated with Corpus and Herbam by the book.
How about some kind of monkey? Could it be argued that a Barbary Macaque has intelligence and a true mind? That would let it fit Mentem. I'm unsure if they're tool-users, but if they are that could possibly be considered Rego. And Gibraltar's not very far away.
Plus, the sheer Awesome Quotient (AQ) would be off the scale!
I'm not sure a familiar can learn apart from the magus. "Over the years, your familiar learns what you know, provided that you keep the familiar with you when you study and that you share your knowledge with it" (p. 105) indicates that it can learn from you when you study (basically, you chat about what you read today), and could be construed as learning from adventure experience when it's adventuring with the magus, but Familiar Education and Advancement always struck me as being overly restrictive, r-a-w.
Realms of Power: Magic (insert, p. 57) has suggestions for Familiars by Art. Rego lists badger, black cat , cockerel, dog, lion, owl, wolf, and any pack leader or similarly dominant animal. Imaginem lists chameleon, cricket, magpie, partridge, peacock, and scitalis (a type of dragon).
Muto lists a white or tortoiseshell cat, fox, hare, moths and butterflies, toad, and other amphibians. Mentem lists ape, black or tortoiseshell cat, fox, owl, wolf, and any animal with an Intelligence score (before bonding).
Although, really, any Familiar-worthy animal can (and, in my opinion, should) have Int rather than Cunning. Not sure an Ent would make a good forge companion, though. "Groot!" "Yes, I need you to stick your hand in the fire again. Don't worry, I'm positive I got the fireproofing spell right. This time.."
Yeah, the RAW is - I wouldn't necessarily say "restrictive", more "vague" - about how familiars learn. For instance, if the familiar has Intelligence, shouldn't I be able to Teach them?
Yeah, the whole "fire plus plant" thing isn't filling me with optimism, although some kind of Fae isn't off-limits. Your lists suggest a black cat, owl or wolf (as ReMe), or fox (MuMe) which are possibilities (although the cat seems a touch dull). Chameleon could be amusing, but probably fails on Technique and "having intelligence". And there's Ape again, but again no technique given.
Plus there's a story seed there... 
Mike the Magic Monkey!
RAW is (was) ever shifting and changing. But as of Through the Aegis, the official word is that magic might familiars have no more learning penalty once bound and made mortal.
Really? I may have to get a copy of Through the Aegis sooner than I planned.
Wossat in English (I'm unfamiliar with the learning "penalty")?
Right, shall we go for a monkey then? Would someone like to take the story?
RoP-Magic introduced the concept of a penalty to advancement of Magic Creatures, subtracting Might Score from Advacement Source Quality. This contradicted the RAW about Familiars, so I ruled "No Penalty if the magus is involved in any way".
In Through the Aegis, there are many example magi and several Familiars. The familiars have more xp that RoP-M suggests, so people were asking about it on Forum. David Chart responded that the rule of thumb used was "no penalty once bound".
So it isn't officially worded, but it is officially presumed, and is the rule used for published cannon familiars from that book.
Anyway, if you lack RoP-Magic, I would be glad to generate a magic monkey for you and work it into a story.
I do lack it (I still only have Core), so that would be top, thanks!
So what's the rule in this saga? Do familiars have the Might penalty to learning or is there "no penalty once bound?"
My take on the rules:
Immortals are almost fixed in stone. They have incredible trouble learning new things. This is reflected in a lot of the 'become immortal' magi options as well.
Familiars give up their immortality to be bound to a magus. Because they become mortal, mutable, changeable~ they can learn new things also. That seems to fit consistently with the spirit of the rules.
Can he be Squirrely?
I shall use that as one of my inspirations.
Also, I favor the ruling of "No Penalty once bound". What do others think?
Works for me.
Fine with me.
And me. As I say, I was hoping I could teach him MT.
Hum... I'd say yes, but.
We've had a familiar trade-of of power vs experience when creating them.
Since we're in a fast-moving saga, this encourages the former.
If that's ok, so be it.
If not, we should work some limitation, such as "no penalty for exposure or adventure xp along the magi, or when taught by them".