If it were me, I’d close all except the Walmart, Cap1 QS, and BBT.
I'll second this... Garden for a year and hit up Cap Ones pre-qual page and see if they offer the no AF Quicksilver to you. Hopefully by then, they'll have the kinks worked out of combining cards and you can merge your QS1 credit line into the no AF (and hopefully non bucketed) Quicksilver. Walmart should grow but you can call the overseas Synch number and ask for a credit line increase to $10K (or $20K... People get quite amazing CLI's using that phone number but YMMV.) Eventually it should PC to a Walmart MC, but as it seems, Capital One will be taking over the Walmart portfolio, so a lot depends on how things are underwritten in the changeover. BB&T just wants to see responsible use of what they've given you, so treat it good and they should be willing to give you CLI's and even another card in due time.
Definitely cut the First Premier card. If I'm not mistaken it's one of those predatory cards. I regret opening a credit one card since I was approved for a cap1 card(which is essentially better) and is also under that category of "predators".
First premier 400 cl. Bal 0 2 months old.
Cap 1 quicksilver one 400 cl bal 0 3 months old
Jared jewelry genisis 300 cl never used 15 months old
Walmart/synch 200 cl 0 bal 3 months old
Bbt cash rewards 8k cl. 900 bal hasnt reported yet .new
Personally I don't use credit cards for shopping as I find myself spending more money using credit vs giving away my Benjamin Franklins. But YMMV. So having said that I would close all store cards.
In terms of the other cards I would determine whether I should keep them based on ability to do product change, delivery of ebills and age of the card. For me the first two are most important as it makes the card more future proof.