I believe that any effort to level up anything other than weaponskill is kind of false economy - weapon skill enhances parrying - it's actually a really good defensive skill itself, having a high weapon skill also seems to enhance the growth of all other skills, especially as the weaponskill becomes legendary+. I speculate this is because a dwarf with higher weapon skill attacks at a higher frequency, meaning the sparring partner parries, blocks, dodges, and takes hits more. So basically go full-tilt maxing out weapon-skill, their high weapon skill will keep them safe through parrying/deflecting, AND, all their other skills will develop faster. Another factor is the "a good offense is the best defense" principle, the quicker your dwarves wipe out the enemy, the fewer hits they have to take. This again favors weaponskill.
With that said - I have found dwarves who don't start with weapon skill can still do respectably. But what I'm interested in is what works most reliably. It seems that an investment in weaponskill is the most reliable and robust.
In terms of embarking with a large teacher squad, there is a benefit in making them all weaponuser-teacher, if you then add new recruits to the squads, the teachers don't waste a bucketload of time teaching striking, kicking, biting etc to the newbie, instead the relevant teachers can focus on teaching the relevant weapon skills. For that matter they also don't waste a bucketload of time teaching each other those relatively useless skills, instead they can start sparring with each other sooner. Sparring is still a very important part of teacher squads so the sooner they get to it, the better. It's probably worthwhile having them teach each other shield user and perhaps dodger, but even then everything I said above about the benefits of a maxed out weapon skill still applies. Of course doing other things is okay for flavor, it's nice having a bunch of kung-fu biter axelords, but I think in terms of cold hard efficiency, weapon skill is king.