Yep, the studies I've seen is for most stats, 300 PA is more than an adequate sample.
The problem is that this applies more to an established player, since 1st and 2nd year players can't be assumed to have stable model parameters, both the player and the league are making adjustments (see Herrera last year).
That's the problem with the sample, but as far as such things as power, it's obvious that Joseph is a plus plus player.
Where minior league stats have value is as a check on major league performance, for example, Hernandez's development his first two "full" seasons in the major correspond to his performance in AAA at a suitable age, which gives you more confidence that he can maintain that level of production (though doing it this year obviously more predictive value going forward than what he did in the minors a few years ago).
On the other hand, Altherr who had a breakout minor league season before one good ML month is an unknown, that could indicate he took his game to the next level or it could be a fluke. Same issue with Pullin, did the light go on or did he just have a hot run that will even out this year?
And you need other information, often pitchers put up bad statistics for the Phillies at Reading, both due to the ballpark but also player development where they stress using secondary pitches such as a changeup when the pitcher isn't comfortable throwing them, instead of relying on their fastball or their best secondary pitch. You often see a meh season followed by a really good season once they've mastered that weaker pitch. Or you get an Asher, who completely changed his approach from a mediocre 4 seamer with velocity, to a slower but harder to pick up 2 seamer. I think they wanted Appel to go back to the 2 seamer that made him a #1 pick out of college before he was injured. That's the kind of information that's hard to gleam out of aggregate statistics, which is why there's a bigger stress on "quality" analytics like velocity, movement, location, effectiveness of different pitches, and for batters, plate discipline, exit velocity, etc. It's not just whether a player performs better, but WHY they perform better.
This is why you have to watch the games - if Appel regains that devastating 2 seamer, everything he's done in the minors as a 4 seamer (the change made by Houston) becomes irrelevant, because he won't be the pitcher who was so erratic for Houston. Eflin has healthy knees for the first time in years, how will that affect his stride, velocity and command? And so on.