What is the "recommended" gear to enter each Turn of Binding Coil of Bahamut?

[Terius]

I'll continue to run AK since it's kinda fast, I still need the Myth tomes and now you just told me all Strategos pieces can drop there. Thanks!

From what I remember:

1st Boss = Gloves
Chest between 1st and 2nd = Earings/Ring/Necklace and Belt
2nd Boss = Legs & Boots.
3rd Boss = Chest & Helm.

As you said it gives Myths too so you'll always end up running it each week. Get your Relic to +1 which costs 900 Myths as it gives the largest initial boost.

And doing all that AK running will net you 100 Phil tomes a go, so you'll have plenty to upgrade yourself with some Darklight pieces too.

You'll want to buy the Darklight Ring & Bracelet first, as the DL ring is unique and you cannot have two, which is why Strategos Ring is your ideal 2nd ring. This means you should have Strategos Earings, Necklace & Ring from AK with Darklight Bracelet and Ring filling out the remanining jewelery gear slots.