Welcome to the boards 
For scoring mix, all you need is an installment (I assume that's what Kikoff is) and three revolvers. You have AC and Disco already. Next good bet is OpenSky - it's a no-credit-check card with a $39 annual fee, well worth it for its purpose.
Very simply, once you have the three cards and the installment, use them all you like but when the statements cut, let a $10-15 balance report on Disco and have the other two fully paid off. This is called AZEO, all zero except one. It helps with some extra points. A good practice to get into would be to make your minimum payment as soon as the statement cuts, so your obligation is done and you can't be late. Then pay off later charges before the due date, in full for AC and OpenSky and all but that $15 on Disco. Long as you pay that off once the statement cuts, you'll pay no interest and preserve your grace period.
Other than that, just do AZEO, make every payment on time, always, not even an hour late, and just cruise for two years. At that point, all your HPs will be gone, you'll have two solid years of perfect history, and you'll have zero derogs on your reports. Sky's the limit at that point!
It will take time to build a profile for the prime cards that you want. I'm not familiar with Kikoff, but my advice would be to let the three accounts you have gain age & and let the inq's you burned before picking them up get older as well. If you garden for at least a year, you'll have three lines with a year of positive payments and your inq's, while still visible to lenders, will have become unscorable. (The inq's will fall off your reports after two years.) Since you've been out of the credit game for 7 years, you're pretty much starting over from scratch, and just like someone new to credit, you'll have to establish history and grow score before the major lenders will open up their rewards cards to you. In the meantime, you actually have a good rewards card in the Discover secured, and you can request they switch it from the capped 2% dining/gas rewards structure to the 5% rotating categories the It CB has, if you think that would work better for you. Additionally, it can graduate to a unsecured card in < 1 yr if your profile supports it.
While you're gardening, I'd suggest researching and reading up on credit scores and credit reports from good sources. @Anonymous's scoring primer is an excellent place to start. The Vantage scores you're seeing from CK have a pretty limited value in judging where you are in your credit journey since very few lenders actually use them. FICO scores are the ones you really want to monitor, and you're not seeing a FICO from EX yet b/c you need six mo's of credit history to generate a FICO score. That's ofc another good reason to garden for a bit, as you'll be spending your HPs on denials for the most part until you actually have a score.
The $40 collection actually isn't counting against score on FICO version 8 & 9, as they discount nuisance collections of < $100. Good luck on getting the $500 CA dropped from EQ. If you run into any trouble with it, there are a lot of good people in this rebuilding forum who can advise you on further steps.
Welcome to the forums, and good luck on your journey!
