I generally agree that a man discerning diocesan priesthood should give first priority to entering within his home diocese or the diocese with which he has the most connections/time spent. However, although thankfully it is becoming less and less of an issue today, I think there are good reasons to pursue incardination in a diocese other than one’s own. And in that vein, yes, perhaps knowledge of the schools/parishes within a diocese is helpful, I wouldn’t say it is harmful to not have such knowledge. But anyway, generally, I agree that one should always seriously consider his own diocese, even if it is more “liberal” than others. In fact, that could be a good reason for an orthodox Catholic man to enter with his own “liberal” diocese - to be an orthodox example to people who need it most.
Honestly, I think it’s a difficult question of which diocese to enter, if one’s diocese is less than ideal. But I think it ultimately depends on each individual man - his strengths and weaknesses, and what he needs most in formation. Formation of any priest is extremely important, of the utmost importance, for obvious reasons, so I believe the biggest reason not to enter with one’s own diocese is not necessarily how “liberal” it currently is, but where they send their seminarians for formation. And if the formation of the seminaries which a particular diocese sends their seminarians wouldn’t meet the seminarian where he is at in each area of formation, then I would argue that is a very, very good reason to not enter in one’s home diocese. The only way to do this is to develop relationships with both the vocation director and the other seminarians from the diocese. The vocation director, because he can help you discern whether or not you should enter with that particular diocese, i.e., whether the formation of that diocese’s seminaries will be adequate for that particular individual; and the seminarians, to get firsthand knowledge of what seminary life/formation is like there. I think it’s important to keep an open mind in these matters, but on the other hand, formation is of the utmost importance!
To give my opinion on your other questions:
Another thought on looking into another diocese - even though I think it’s legitimate to look into other dioceses with which one has little to no connection, I think it’s difficult to do so, because the vocations director of the other diocese has to be open to accepting “outsiders”, and especially if you have absolutely no connection to that diocese, he will probably be very hesitant. However, I don’t think there would be any harm in contacting that particular vocations director and asking him if he considers men outside the diocese, and if so, you could set up a meeting with him, during which you could express your concerns with your own diocese. Either he will agree with you to some extent and consider you, or he will “set you straight” and say you should just go with your own. Regarding visiting seminaries, I can’t say for sure, but I think it would be hard to set up a visit outside of a diocesan sponsored visit. But again, that’s something you could look into - look up the potential seminary’s visiting policies, if you can find them.
Similar to things I’ve already said - I think it depends on the individual. I think for some it can be good to enter right out of high school, and for others, maybe not. This is something a vocations director could help you discern, along with your individual spiritual director, if you have one. In any case, as far as I know, Benedictine College would be a good place to continue discernment.
Regarding seminary dress, while I don’t think that should be the sole reason one decides upon entering with a certain diocese, I think it plays a part in the bigger issue of formation. Personally, I think it is great for a seminary to require a cassock more than just for liturgy, as it can serve as a constant reminder of what one is doing there in the first place, and as a reminder of who he is and who he is going to become after ordination (God-willing). I think dress is extremely important. Probably the same people who don’t like the cassock or who think seminarians (or priests, for that matter) shouldn’t be required to wear it also believe it’s ok to look shabby for Mass. Because “it’s only the intention that matters” and “it’s between them and God” - that kind of thing. But the reality is, one’s clothing can and does affect the way one thinks.