You seem to be well on your way. The only thing holding you back is history. However, I think all of the cards you mentioned can be in play. I can't speak to if the needed history is an issue with them or not, but you are well within range for those cards from a score perspective.
What about CAP1 Venture card? By the way I am coveting those scores. 
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@Anonymous wrote:It's been a long six months! I was going to wait until I got the CLI on my cap1 secured card, but figured what the heck and signed up for CCT. Survey says, TU 750 EX 769 EQ 750. I was floored, to say the least, with only one card and a scant six months of history. Many thanks to everyone here who consistently offer advice and support, without which I would never have taken that first step. Now, it's time to build on that good start without going overboard or messing up.
Oddly enough, cap1 didn't pull EX when I applied for the secured card, hence the higher score.
Soooo, the big question is where to next. I ran through several preapproval sites and got the following:
CAP1: Platinum and QS1
Amex: Blue Cash Everyday
Discover: IT
No go on Chase. Alas, Freedom is one of my "mini goals." I thought about apping anyway but I don't want to press my luck since I hear they prefer to see closer to a year of history. Not sure what to app for and in what order, but it's time to replace the secured card.
Well done. I would cold app Venture and QS (forget the rebuilder cards). BCE is good. Discover is iffy about history, but go for it. My mom qualified for the Freedom card with just AU history from me since she hasn't had a credit card in years. She also got the Walmart MC and PayPal MC (her scores turned out better than mine, but she doesn't have any baddies). Barclays likes a year of history, so wait and then go after the Arrival Plus card. Citi likes to look at probably a years history also, unless they have blacklisted you. For longterm planning I would fill out a members application with PenFed ( if you pay $10 or $15 for one of their pet projects, they will let you join) then go after the PenFed Promise or Platinum Rewards Visa. Good luck and have some fun.
I would tend to disagree here. Even with those scores, the OP has a very thin file, and may not support those cards yet - I would instead, suggest apping for the Platinum and QS1, closing out the secured card if needed. Then in 90 days or so, app for the QS Visa or the Venture, whichever one fits the OP's spending habits. Remember, this is not a sprint, its a marathon.
I didn't have a $3k or $5k bank card when I got approved. My highest approval was a $2k Barclays bank card. My store cards were over that amount, but Cap 1 was the only one willing to give me a higher limit bank card. Cap 1 will no doubt open up the door for him for good approvals for Chase and Citi, but he needs a prime card under his/her belt.
That may be true - but I just believe its wise to chart a conservative course. Crawl before walking, walking before jogging, jogging before sprinting - that sort of thing.
We can agree to disagree. When I finally get my scores to that level, there isn't too much left that I would like to get. PedFed and SDFCU are primary on my list, and maybe Citi, but I have the cards I need now. Got a RSVP from Amex yesterday for a Platinum card. Think $450 annual fee is too rich for my blood. 
Once again, thanks all. Lots to think about. Probably for a few days, it's not as if those prequalified offers will go away. Speaking of which, how solid are they in the first place? Other than cap1 that is, since it's it's likely they'd approve the platinum with a decent SL. So many more questions...
Would it be worth it to app for QS and fall back to the platinum if denied, hoping for a single set of pulls? Platinum and QS1 probably won't fly since that would make three subprime cards. Apping for platinum, cancelling the secured card and then apping for the QS1 would throw another six HP on, so not thinking that would be a great idea.
I still want the freedom, I think I'm going to have to curb myself.