@Anonymalous, for most cards, I'd suggest applying when your older card is a year old and your newer one is six months old.
Discover would be an exception. I think you could grab that right now. Check their pre-qual. If you grab Discover now, wait six months before your next application.
Don't think about US Bank unless you've gardened for a year. You'd probably also benefit from the thicker file you'll have down the road.
More good advice, thanks. The denial I got from Chase was for the Freedom Flex, and the Discover It seemed like a good alternative, so I tried the prequal shortly after. But while the usual cards showed up, I changed my mind and decided I didn't want to deal with rotating categories. That's why I had my eye on the Citi Custom Cash, with a category based on spend; and on the Elan Max Cash Preferred, whose categories are set once and then persist (which is apparently not the case with the US Bank Cash+). Oh, well. Maybe in the future.
Though if I were starting all over again, I might have gone with Discover as my first card.
IMHO, I would add a card or two now so that they begin to age, and be concerned about building your credit on a long term basis, and not so concerned with rewards. Discover & FNBO may be a good option, if you have medical, dental or vet bills Care Credit may be one to consider.... though it's Synchrony that line usually grows rapidly.
I would even consider a "self lender" type of loan, for the highest amount you can deposit monthly, that the bank or credit union allows. In 12 months.... you'll be in a whole different situation.... in 12 months it shows as the loan was paid in full and helps on your build.