So my first two actual credit cards are from my local credit union and the Quick Silver card from Capital One; the rest are revolving accounts except that loan one so with chase, I think I'm at 4/24.
Side note, yes I'm open to business cards (since I'm actually building up a registered business) but I didn't include it above since I doubt I'll get one at this point in time espcially from Chase.
Have you checked the online pre approval pages for Amex and Capital one?
Chase >> I recommend in branch personal banker pre approvals.
Have you thought of a Discover Card? (just throwing stuff out there)
Personally, I would suggest that you check in-branch for a Chase Freedom pre-approval since getting any other card for a while would put you at 5/24. If one doesn't exist, I'd probably take the HP (or two) to try for it.
For Amex, do you currently have any pre-approvals showing on their website? You have both Blue Cash EveryDay and the EveryDay card listed. Before going for an Amex card (other than a cobranded one, i.e. Delta, Marriott, Hilton), I would spend the time to research and decide whether to go with cash back or Membership Rewards. You can't product change between those products later and unless you are putting quite a lot of spend, it may not make sense to mix and match MR and cash later if you decide to get more Amex cards.
If there's no Chase branch near you, sign up for Chase Credit Journey. Preapprovals can come through there as well. Also check the "Just for You" section of your online Chase account for an offer with a green check mark on it (those are as close to a guarantee as you can get) that just asks a few questions like income and housing.
If no preapproval looks like it's happening I would just try for the Chase card since getting any other card will put you at 5/24 for quite a while. If getting new cards isn't urgent, the more time you can put between your new cards and application the better.
Not showing any green check marks, just the white and black star that says "You're prequalified" but in the Credit Journey since I've been had it has a little meter over the ones that I'm prequalified for and those are the Chase Freedom Unlimited, Sapphire Preferred and the Freedom. All three of those has the meter in the dark green for "Your approval odds".
The black star offers are more or less synonymous with the green check mark offers, I believe. If you click on one does it just ask for very limited data? If so that is a really good sign.
Anything showing approval odds wouldn't be a real preapproval.
The Freedom card always struck me as too much effort for too little return (the category earnings are capped). Without a Sapphire card to which you can transfer the points it is even less attractive. The Freedom Unlimited is a decent card, but you already have 1.5% with the QuickSilver.
The Savor One complements the QuickSilver nicely. The Savor (non-One) is only worth if it you spend enough to justify the fee.