I would take into account any AF's or high APR's to consider before closing in the event that may need to continue assisting you ill Dad with credit.
If you'll be fine without them, I would agree to close them all as they'll remain on your CR's for another 10 years after the closed date. Be sure to give some time for everything to report to assure that all is IDEAL before proceding to apply for a prime(s) card.
IMO, wait until you obtain the card you have in mind and then close the creditone as I'm sure that card probably has a high APR and AF right?
"When you're fresh meat you kill... and give them something fresher" (Frank Underwood)
I would ditch the cards with annual fees.
Run, don't walk to close Credit One! Don't worry too much about aaofa at this point...remember they will still report for ~10 years and by that time you will be sitting pretty with multiple prime cards with nice limits 
Get a Discover card, get in the door with Chase, and perhaps Citi. Ditch your cap1 and credit1 cards. Beleve me when I say you are not going to need them or want them. They will still piss you off even in the sock drawer!
Thank you for all the responses!!!
Cap 1 does not have an AF. They've been good to me so far, gave me unsecured less than 1 month post BK (which is 4.5 years old now), then gave me regular CLI but I think I've hit the max they give on that particular card.
I don't think Chase is bk friendly and they are the ONLY reason I had to file BK... that story is buried in here somewhere and an attorney was involved to retroactively sue Chase. Someone at the bank was fired over the issue but I remain with a BK on my credit. 
As for Discover, I did not think they were BK friendly either??? If so, what score is required? how much time after BK discharge?
I'm trying to get myself in shape for 1) a mortgage and 2) a prime card. I had read on here somewhere that if a prime sees you still have $300 and $500 limits, they won't give you much either.
As for my dad... that situation is done. He is alive though ill. It was a sequence of events that led to me living on my credit cards (and keeping them paid on time). Two months without income + gravely ill father + 1500 miles away + living in hotel to help Dad = credit card maxation (should be some economic theorem for that!)
@Hopelives2 wrote:
Card Limit Balance Cap 1 2250 0 Cap 1 v 2 320 0 Cred 1 1050 0 Tires Plus 900 0 First Prem 500 0 BBY 300 0 Care Credit 500 0
The cards in purple, I was going to keep open until I can get a prime card.
The others I was going to close after the payments post. Eventually, I'd like to get a better Cap 1 card, and get rid of Credit One.
Thoughts?
Called both BBY/CareCredit, closed both. Both asked why, I said, "The credit limits are an embarassment." The customer service agent had no response.
My $10 fee with FP showed up so I'm going to pay that today, wait for it to post and then call them.
Cap 1 v 2 is an old Orchard and next up as soon as $0 balance clears.
Tires Plus has no fee but ... closing them too.
That will leave me with Cred 1 and Cap 1. $3,300 available revolving.
Hopefully, my score will increase substantially. From maxed+ to $0 in a matter of 2 months
@Hopelives2 wrote:
@Hopelives2 wrote:
Card Limit Balance Cap 1 2250 0 Cap 1 v 2 320 0 Cred 1 1050 0 Tires Plus 900 0 First Prem 500 0 BBY 300 0 Care Credit 500 0
The cards in purple, I was going to keep open until I can get a prime card.
The others I was going to close after the payments post. Eventually, I'd like to get a better Cap 1 card, and get rid of Credit One.
Thoughts?
Called both BBY/CareCredit, closed both. Both asked why, I said, "The credit limits are an embarassment." The customer service agent had no response.
My $10 fee with FP showed up so I'm going to pay that today, wait for it to post and then call them.
Cap 1 v 2 is an old Orchard and next up as soon as $0 balance clears.
Tires Plus has no fee but ... closing them too.
That will leave me with Cred 1 and Cap 1. $3,300 available revolving.
Hopefully, my score will increase substantially. From maxed+ to $0 in a matter of 2 months
Closed First Premier. 
Agent: "You do realize that this is one of your oldest cards."
Me: "Yes, please close it."
Agent: "Well, it would help your aging of accounts and your ratio of credit limits to current balances."
Me: "Yes, I know. Please close it."
Agent: (no doubt she's soft pulled my credit): "Are you sure because I could waive $25 to your account which would cover the monthly fee."
Me: "Please close it."
Agent: "I really think you should reconsider."
Me: "Please close it."
finally...
Agent: "Your account is closed. You can reopen within 90 days with no additional cost or credit review."
Me: "Thank you. I see there is a credit balance. When do I receive that back?"
Agent: "Within 60 - 90 days."
LOL - SOOOOoooo they are going to keep my money. Alrighty then. Wonder if I can charge them a monthly fee for the interest they are getting on it?