If you can't afford a Circlet of Shadows (instant clicky invis at lvl 20), which is likely if this is your first toon, then invis is level 30 yeah, although you get IvU earlier. It's no biggie though, you can always snag a port to go to faydwer.
You're right in thinking SKs don't have too many spells as you have way less than the necro you're pumping em from. It's just the right mix at higher levels of a good toolbox without needing to swap spells constantly either.
As to the pet, you do have one but see it more as a dot than a pet, really. The pet is OK at lower levels, becomes utter crap mid game and is excellent at the latest levels.
If you have any questions don't doubt asking me IG if you need guidance
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Cheers;