I will do a little bit of thread-o-mancy here, as this discussion has attracted my interest.
Regarding how those different virtues could affect character generation during apprenticeship, I would use these rules :
Secondary Insight : for each 4 points of experience put into Arts, the character gains an extra 1 experience point. The extra points can be distributed freely among the arts, but at least among 4 different forms and 2 different techniques.
[i]Justification : Assuming that the character has spent an even amount of time learning techniques and forms, the virtue provides an average 3 extra exp per season of study. I assume an average quality of 12 for his source study. During apprenticeship, that would be the parens teaching source quality : 0 average communication + 3 average teaching + 3 + 6 bonus for teaching to only one student.
So, each time the average master spend a season teaching an art, the character gains 12 exp points + 3 average extra points from his secondary insight. Thus the ratio 1 extra point for 4 points expensed at creation.
Of course, the apprentice could also have learned from books if the master had allowed so. But I assume the apprentice learns quasi exclusively from teaching. Even if a significant time is passed learning from books during apprenticeship, we could assume the same source quality for the sake of simplicity.[/i]
Elemental Magic : for each 4 experience points put into elemental arts, the character gains 1 extra point. The extra points must be distributed equally among 3 or 4 elemental forms.
Justification : the same reasoning as above. Elemental magic provides 3 experience points when studying one elemental forms, which are distributed equally among the other 3.
Book learner : for each 10 experience points put into an art or academic ability, the character gains one extra point into that art or ability. This could extends to other abilities with the storyguide consent.
Justification : book learner provides 3 extra points when studying from books, which often relates to arts or academic abilities. For the art, the same reasoning as for the two previous one would apply, but since a newly gauntleted character had learned essentially from his master's teaching, the bonus is lowered to less than a half. For academic arts, the setting is more arbitrary, but one could argue the same : a young character has learned essentially from his teacher(s).
Apt Student : for each 5 experience points put into an art or academic ability, the character gains 2 extra points into that art or ability. This could extends to other abilities with the storyguide consent.
[i]Justification : Same as above. Having learned essentially from teachers, a newly gauntleted magi would benefit more from this virtue than book learner. Apt student add 5 to the study total. With the same average source quality of 12, this translates to a ratio of approximately 2/5.
This setting makes this virtue very attracting to young hermetic magi compared to other virtues like book learner or free study. But this seems balanced to me as Apt Student is unlikely to be as useful as the latters in the life of an experienced magi.
Note that in order for this virtue to give the same number of extra bonus experience as Skilled Parens, the character would have to spend 150 experience points in arts and/or academic abilities. But Skilled Parens also give 30 spell levels and a close relationship with a powerful magus. Still, one could increase the benefits of Skilled Parens to maintain balance, maybe to 75 experience points instead of 60, and 50 spell levels instead of 30.[/i]
Free study : no extra benefit. Apprentices do not learn from vis so this virtue is unlikely to have been of any benefit during the apprenticeship. Eventually, one could argue that the master may have given the apprentice a few vis pawns to play with just to learn the basics of free study. If so, this virtue could provide a very small fixed amount of extra exp in the arts, around 5, may be up to 10.
Study bonus : for each 15 points of experience put into Arts, the character gains an extra 1 experience point into that same art.
Justification : study bonus provides 2 extra experience points when studying from books or vis. As mentionned before, a newly gauntleted magi have learned essentially from teaching, so may not have beneficiated much from this virtue. So I have applied the same rule as for book learner, and since study bonus gives only 2 extra exp, the ratio become 1 for 15 instead of 1 for 10.