You can just include your spouse's income in with your total income when applying for the card. Assuming you're both over 21, I'd also assume you both have access to one another's income in a way that lets you include your spouse's income in determining how you, as a household, pay bills. Dug up a NerdWallet article that explains it a bit:
https://www.nerdwallet.com/blog/credit-cards/list-spouses-income-applying-credit-card/
It could be worth creating a free account with a service like CreditKarma or NerdWallet, or even a paid one with MyFICO, to keep close tabs on what your credit score is up to. Though something like CreditKarma actually shows you the "VantageScore" (not quite FICO), it at least gives a fairly accurate picture of how your score might be moving up and down, what factors are currently impacting it, and what your FICO score would look like to a lender at any given moment. Then you could time applications accordingly - a balance change on another account or some older item dropping off boosting your score a bit and making for a better time to apply. The good thing about MyFICO is it updates realtime (though that is a feature you have to pay for), while something like CreditKarma updates weekly.
Something that's handy with some of these free services like CreditKarma and NerdWallet is they have credit card search and information tools - a single place you can go to look up CCs, sort by features (no foreign transaction fees, no annual fees, etc), and can often get estimated approval chances based on your credit profile.
Taking a quick look at them now myself, I see the Chase and Capital One cards you mentioned, along with a couple Bank of America cards, the Costco Visa, a couple American Express cards, the Wells Fargo Amex, Mastercard Gold/Titanium/Black cards, World of Hyatt card, Alaska Airlines Visa, the HSBC, and a whole host of others. Keep in mind sometimes you're trading a foreign transaction fee for an annual fee. Also keep in mind, while branded differently, some cards are issued by the same institution (Chase has some hotel and airline cards, for instance).