I think that part of the problem here is that some people are placing too much emphasis on the word 'type'. The quote includes the phrase 'choose one type of weapon...'
I suggest not over-thinking this phrase, but just choose a type of weapon, naturally. Remove from the equation any context of D&D and PF, and just choose one type of weapon.
Do it... right now... Choose a type of weapon.
What did you choose? Did you choose 'all weapons that deal blugeoning damage'? Or did you choose, say, a mace? Probably not the former, as that is actually a 'category of weapons' and not a 'type of weapon'.
I believe that sometimes these sort of tactics are commonly used by rules lawyers {which I, of course, am} for the purpose of taking advantage of the rules and exploiting cracks in an otherwise fine system.
Here is a somewhat unrelated example:
Consider the sentence
'I didn't say he beat his wife.'
Now, consider emphasizing each word in turn, and saying the sentence again.
'I' didn't say he beat his wife.
I DIDN'T say he beat his wife.
I didn't SAY he beat his wife.
I didn't say HE beat his wife.
I didn't say he beat HIS wife.
I didn't say he beat his WIFE.
Note how every time a new word is emphasized, the meaning of the sentence ENTIRELY CHANGES.
So, to get back to the argument:
'CHOOSE one type of weapon'.
Do not 'Choose one TYPE of weapon'.
Keep It Simple, Silly.
Add to this the evidence easily available in the bestiary {i.e. Weapon Focus (Longsword)} and the meaning of the RAW should become clear. If it still remains unclear, go back to Rules Lawyer School. I'll be there, we can do lunch.