Yep, designing the grog and servant would be good. Basic rules for them is that the grog is a shield grog, he's there to defend you. So he shouldn't be an archer or something else that isn't suitable to protect you from physical attacks. The servant, for his/her part, should be someone who handles day-to-day affairs for you. Cleaning your clothing, feeding you, arranging lodging, etc. After all, magi are so useless at those tasks if left for themselves.
The servant can easily be a bit older, with some useful skills. But probably not litterate nor any kind of teacher. Someone who won't mind getting his/her hands dirty for the magus.
As for visiting rules (for advancement), remember that things must be paid up-front. Arrangements are possible, but usually less favorable for the visitor. And you won't know about the exact stats of a book (or teacher) until you are commited for the season. So taking your example, if you were to visit a covenant in the hopes of studying from their library and use of a lab, you'd need to first pay for your year's stay there (3 pawns or 1 season of service). Then, pay for access to the library (1 pawn per season) and the lab (also 1 pawn per season). And they might not allow you to extract raw vis from their aura for your own use, depending on that aura's strength, as some believe that too much extraction can weaken an aura -- so those covenants tend to restrict that lab activity to their own benefit.
(Yes, established covenants milk visiting magi for all they are worth. That's a way to "encourage" independent magi to join as members -- which has its own set of constraints, particularly for the younger ones.)