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While I would rely on more experienced members to advice on the other aspects - please don't close the secured card. Let it go on for some more time as AAoA is also important for a good credit score.
Since you already have Capial One you might want to try their pre approval link, from what I hear it is very accurate and if it reccomends a card for you it will probably be an approval. Several other companies have the pre approvals such as Chase, though they can be picky about lenght of credit.
I say apply for Discover and Barclays. From what I've read your thin profile may be attractive to them. But as someone previously mentioned, checking the pre-approval site may get you a good result too!
Here is a link to a topic that has a lot of pre approval sites and some that have experinced them. Most of these pre approval links are soft pulls, possibile all of them, and the hard pull does not come until you officially apply.
http://ficoforums.myfico.com/t5/Credit-Cards/Pre-Approval-Sites-June-2015/td-p/4059266
You do not necessarily have to keep the secured card open as it will remain on your credit report for 10 years after you close it. However if you are going to close it, do it a few months after you are approved for the cards you want.
I would say 3-6 cards from different banks in one app spree, as your AAoA is going to tank if even one of them report.
Although I am unsure what your general spend is, I would try for these cards.
Citi DC- 2% General Spend
Amex BC or ED (Groceries or just to have a growable CL)
Maybe a Discover It for the bonus categories.
Capital One Venture+Capital One Quicksilver/Venture One-Relation+Bonus+Account combination+Possible 2 cards for 3 HPs
If you plan on getting a Chase UR card such as the Chase Freedom or CSP, be sure to apply for it before before having 5 accounts in 2 years. However do note that some have reported that they like to see a year of history.
As always, check for any prequals before applying.
The Discover pre qual site is no guaranteed at all. My dog has an offer on that site. However, Discover like thin files like yours. Capital One is another good lender, seeing that you have done excellent with your secured card, I would go for what they have offered you.