Keep in mind that most spells are usually taught late in apprenticeship, because otherwise the apprentice would be limited to only the lowest levels.
I guess one question is whether an apprentice can be considered "relatively weak." That seems to me dependent entirely on where in the apprenticeship you are. Year one? Probably pretty weak. Year fifteen? They're practically a magus in their own right.
One thing that would be sure to generate stories is if her Gift ends up being flawed (or is damaged during apprenticeship), causing her to fail at becoming a full maga.
Taking that flaw with your apprentice is certainly a risky move!
Maria filia Calpurnia ex Verditius
While Calpurnia's (rare) presence causes people to take an involuntary step back, Maria turns heads. She's stunning, with perfect skin, even white teeth. Her ears are just pointed a bit. She's a hair taller than her mother, at 4' 6". Maria likes to play, and is not sure she wants to spend a life in a tower studying old books. She doesn't like how the Gift makes people distant from her. Maria tries to be careful, when she sneaks off, but knows that her mother can see everything with her helmet on, except her.
She's a trifle ticked about how when she actually kissed a boy, Calpurnia created a statue of him (spontaneous CrTe, and Calpurnia has a +12 Int+Finesse for this) and then shot the statue with her magic bow. The arrows sank in the stone, such that the tips emerged on the other side. The young lad got the message.
Nothing however, has been better than flying around, even if it's in that hideous metal boat. Scrubbing off the rust on the boat is the punishment detail at the covenant.
Characteristics: Int +2, Per 0, Str 0, Sta 0, Pre +2, Com +1, Dex 0, Qik 0
Size: -1
Age: 15(15)
Decrepitude: 0
Warping: 0(0)
Confidence Score: 2(5)
Combat:
[tab][/tab]Fist: Init 0, Att 0, Def 0, Dam 0
[tab][/tab]Short Bow: Init -1, Att +4, Def 0, Damage +6, Range 15
Soak: 0
Virtues and Flaws: The Gift, Apprentice, Faerie Blood (Dwarf), Self-Confident, Venus' Blessing, Covenant Upbringing, Optimistic, Small Frame
Personality Traits: Optimistic +3, Fun-loving +2
Abilities: Athletics (Running) 1, Concentration (Spells) 1, Finesse (Terram) 1, Folk Ken (Adults) 1, German (Excuses) 5, Latin (Hermetic Use) 3, Magic Theory (Items) 3, Order of Hermes Lore (Rules) 1
Arts:
Cr 7(+4), In 0, Mu 0, Pe 0, Re 16, An 0, Aq 0, Au 0, Co 0, He 0, Ig 5(+1), Im 0, Me 0, Te 5(+1), Vi 0
Spells Known:
Coat of Prometheus (CrIg 5) +12 (MoH, p. 110)
Shattering Touch (PeTe 5) +5 (Apprentices, p. 47)
Unseen Porter (ReTe 10) +10
From a Hermetic standpoint, Maria is not "filia Calpurnia" since she hasn't completed her apprenticeship and become a maga of her own right. She would be known as "discipula Calpurnia" instead. 
Who would want to kiss a Gifted girl? She's creepy.
And let me add, again, that if the particular character concept doesn't need a ship, it doesn't have to supply/build the ship. I can provide all of the resources necessary to move the characters to the saga's story location. There's no need to do that heavy lifting as your character, unless that's part of your character. I see the creation of one ship, and a bit of Shipwright experience, but not much else that follows in that ship building vein.
There are two ability scores that are questionable, as to whether they impact the character. I'm noting that there's a fair amount of metal craft, but her Craft ability for Blacksmithing is pretty low. Also, her Major Magical Focus seems to somewhat go to waste, since most of her spells are around 20th level, and her casting totals (and by extension her lab totals) for these spells seem to be overkill. Granted, it's useful on Edge of the Razor, but little else, and Crystal Dart doesn't get the benefit of her focus. I'll point out that you spent 75 xp on Finesse, while probably the most important Ability score for a Verditius is their crafting ability (abilities). There's nothing inherently wrong with the character, she just seems a bit unfocused, or spread thin. In my experience it doesn't make sense for Rego crafting to integrate with House Verditius. The Rego Crafting rules are a bit of a mess, but my experience, and Arthur can attest to this, as we've discussed it before, is that you really need insanely high Finesse totals to do useful things. Even looking at Hermetic Projects section on the Hermetic Shipwright discusses the finesse totals necessary to use Rego Crafting to repair or even build a ship and they are high. A Finesse total of 8 for a Rego Crafter with 0 Perception means, on average, you can expect a total of 14 on the roll, 17, if you're willing to use confidence. Really useful things require totals in the 20s, generally. You might counter that you can retry the attempt, and you wouldn't be wrong, but that runs into the area of the Monte Carlo situation I want to avoid and would trigger the fatiguing rules for repeated spell casting.
And, by your own admission, the Automata rules aren't what you thought they'd be. This might be a good time to sit back and re-evaluate the character concept, because, as I said, you're spread a bit thin.
First of all, I want to thank you for offering me a detailed critique. As I mentioned, this is my first Ars Magica character, and my inexperience shows.
You're correct about being spread thin, and a lot of that is due to the Automata. I really wanted to remote-control it, which drove the need for skill at Imaginem, which meant I needed a talisman so that I could cast a level 35 CrIm spell reliably. Getting rid of it would free up several years that could be better redeployed (not to mention saving 37 vis!)
As for the rest of your suggestions, I will consider them carefully. An improved Craft would make item creation easier, and if I'm going to use Finesse for crafting, my Per really needs to be higher.
As for the ship, I understand that it's not necessary at the start of the game. It is a statement of Calpurnia's power, and possibly a very strong base of operations. I envision that we'll need to explore various places and having the ability to fly many people around would be helpful. However, if it's something that doesn't fit in your saga, let me know, and I'll fix it.
I've personally experienced playing a character who was so spread out as to be able to nearly do anything, but unable to do anything exciting or interesting. In Ars, specialization is really a big deal. Don't have your magus do something you think other magi are doing, because you think it looks cool. Pick one thing, and do it really well. Pick a second thing and be good at it, and then pick a third thing that you're competent with, and all other stuff just doesn't matter.
I'm involved in two Hangout sagas, one I play a weather maga (MMF Weather) who can get like 50+ Penetration on the Incantation of Lightning and has sight and Group and Group +1 variants. But she's also used that spell in diplomacy, too. A prince of Riga had captured a maga who was lying about us to save herself. We asked to witness her accusations, and I said, may God strike you if you lie. She proceeded to lie, and with a Finesse roll, the SG allowed me to make the lightning appear to come from someplace other than my character. She cast it without penetration, so the maga accusing was wasn't injured or otherwise harmed and didn't risk a Code violation. To this very day, nearly 20 years into the saga, she still has 8 Arts that are below 5, and thus can't take an apprentice without some horrible deficiencies. The other saga is a Corpus specialist who wants to solve all of his spells with Corpus. He's basically celibate, too, but had a baroness coming onto him, so he spontaneously cast a spell that, well, satisfied her. Of course, that creates more problems, but hey...
As to the base of operations, well, that's what the covenant is for/will be. If you need ships, or you're concerned about being stranded, take my assurance that you won't be.