A bit late since the OP has already made a purchase but my fav's are Krieger(a bit spendy) White Oak and X-Caliber
Maybe you missed this part:
I want it to be good quality, but I’m not looking to spend top dollar; just good quality for a good value. I’m unsure of which brand of barrel I should buy. I’m considering Ballistic Advantage, but will spend more for a Faxon or even Odin if they are so noticeably better. Thanks in advance.
Had it been any barrel on the face of the earth at any price, that you can buy right now, I would have just suggested the Shilen on gunbroker for $4xx.xx. And then I would have disregarded his 16" requirement and told him he needs to just buy a 20", but I don't think that's what he wants either...