As far as getting HQ, I'm guessing you need at least some woodworking to try it. I'm 40 levels over the cap, and not only did I not get a HQ on several dozen attempts, I actually broke a bunch. I was getting .1 woodworking skill so I guess maybe 5 woodworking (total guess)
As far as leveling, its too component expensive. Go with
I was able to craft this with 0 woodworking skill. In fact, I got a .1 skillup when just using the luan lumber. This is a lumber synth you can do at level 0, so you are safe to make these here and there. I don't know that I'd skil up on them - there just weren't any tekko for my low-level MNK available, so I made them.
I have not made these yet for skill up but i will try tonight, i so far have used the head part of this set as a skill up item and it worked very well.