@Ezk37 wrote:I have listed here the cards/limits I have currently. Any advice on what card I should set a goal for next?
First, welcome aboard! 
Next, there are so many variables, it's hard to give you a meaningful response without knowing a little more about you and what you're interested in achieving as far as credit goes. *MY* favorite card won't necessarily be YOUR favorite card, or even a good fit.
One thing I would focus on is quality over quantity. For me, I'd rather have a small handful of really nice cards than 100 crappy ones!
Have you thought about what type of card you'd like to get, i.e., cash back or miles or points or....whatever? Are you more interested in getting cards with great SUBs (sign-up bonuses) but not necessarily low APRs, or cards with low APRs but perhaps not great perks, or what?
If I were you, I'd definitely get rid of a few of your current cards, i.e., the 'starter' cards, like Fingerhut and secured cards. Work on increasing your credit limits on cards you want to keep long-term. As your credit improves and you can get approved for better cards and higher limits, either close the bad ones or sock drawer them. (I'd close them--they have such low limits I wouldn't worry about the negative impact on my credit score from closing them.)
Let us know what your objectives are, what you'd like in terms of what a card offers, and I'm sure you'll get a plethora of suggestions!
Well score isn't driven by number of cards, or even total credit limits. It's driven by payment history (35%), amounts owed (30%), length of credit history (15%), New credit (10%), and credit mix (10%).
Also, closing accounts won't hurt your AAoA. If they're in good standing, they'll remain on your reports after closure for up to 10 years. So, nothing to worry about there.
My advice would be to close cards you don't need/see yourself really using anymore, but maybe not all at once. Maybe 1 or 2 every few months.
@Ezk37 I would get the Citi Double Cash for everyday spending, then I'd focus on specific perks(gas-transit, groceries, dining...); each card has its on strengths and weaknesses.
I recommend you apply in no less than 6mo(better odds of approval, higher limit and lower apr), until you have a thick profile.
I'm considering closing my starter cards too.
@Ezk37 wrote:I'm aware that I need to have a decent mix of installment/charge/department store accounts as well? So I would need to calculate any closures carefully. Would you suggest taking the hit on the older accounts even if I'm sure I could sock drawer them for eternity?
On your first point--and you'll probably get disagreements on this--I've found that it doesn't really matter what kind of 'mix' you have. Speaking strictly for myself, I haven't had a loan of any kind (car, mortgage, anything) in YEARS (they fell off my reports a long time ago), and that hasn't affected my score at all; it's generally in the high 820s. I do have a mix of major credit cards and a few store cards, but no loans of any kind.
On your second point, a few things to consider if you're going to use the sock-drawer plan: does the card have an AF (annual fee)? If so, get rid of it. Verify with each creditor how long their period of inactivity is, and make sure you use each card during the appropriate time frame. For example, if a card automatically closes after one year of inactivity, make sure you use it at least once during each year. I actually remind myself when a card is approaching an inactive state, so I won't accidentally let it close! There are all sorts of other methods to keep a card active, such as charging an annual subscription (Amazon Prime, for example) or even a small, recurring monthly charge. I go with the "remind myself" method and that works out fine.
All things considered, I wouldn't worry about adverse effects on your credit age by closing any/all of the cards you don't want. It will cause a minor, temporary dip, but shouldn't be a big deal. I played around with a simulator recently, plugging in closing my oldest card (a 30-year-old Discover More card), and it dropped my score by 1 point! 
@Ezk37 wrote:Thank you guys all for the info! The help is appreciated. What is the main purpose of closing unused accounts? Will it increase my chances of higher limit/better cards going forward? Or is it just because they aren't needed?
It's really a matter of personal choice. The cards I have, but almost never use, I'm keeping because of their impact on my total amount of credit (their credit limits are all in 5 figures); I don't want to lose that. But if I had a card with an annual fee, AND it was no longer serving any real purpose, I'd probably close it--even if losing it did have a painful impact on my total credit. But other people would keep them. It's so personal, depending on your needs, and your resources, and all sorts of stuff! Also, if I had any 'starter' cards and/or cards I didn't consider desirable, I'd want to lose them as soon as feasible, in other words, as soon as they're no longer serving any purpose (like rebuilding credit). I just wouldn't want to see them any more!
As for increasing your chances for future cards, having several may or may not help. Some people are declined when they apply for a new card and the reason cited is "too many credit cards," while others have 50, 60 or more cards and don't have any issues. 
@Anonymous, well said, my thoughts exactly!
