Before everything – ask for a CLI
You’ve had the Capital 1 for 2 years with no CLI? Before applying for a new credit card ask for a CLI. Most likely you’ll get one. You can start with customer service, but if you don’t get what you want bypass them and and email the EO directly. Ask for $3k and pc to the quicksilver as a starting point, and they will come back to you with a counter offer.
As to the late payment, it is dragging your credit score down. The good news is that a year from now its negative effect will diminish significantly so you should be able to see your credit goes up, along with the new higher CLI.
As to your question, secured vs conventional credit card, it won’t make too much difference. 3K-5K tied up in a secured card is a lot of money that isn’t working for you, and there are better ways to diversify your credit. For example, you can try a near by credit Union, or maybe a Walmart credit card (and get a free credit score from TU along with it).
Secured credit card should only be applied to as a first CC, if that’s the only card you can get. Certainly not a second or third CC.