I would put a ton of use on the barclay, and make sure you are paying it off, a few times a month if need be. They will give you a nice CLI. They gave me a 3x on my 6 month, and then after a call to underwriters, I got another 2.25x 3 months later.
On the flip side, if you apply for too much new credit, without having a solid history with them, may scare them off.
Focus on the CLI with what you have now. Solid advice given. Then... go for the big boys, Amex, Chase, etc.
In reality, Discover is not offern much in terms of rewards or perks, a basic 1x cash back card with rolling categories. Your goal is to pay in full every month, so rewards is what matters.
