I need help. This is an area I know absolutely nothing about, and I know a lot if you are very knowledgeable about - so please help me?

Ok, here's the background. DH and I are both young and have no debt of any kind. DH has no credit history whatsoever, and works full time but for a very modest wage.
I do have a short credit history - I got a store card 2.5 years ago, used it for s big purchase, paid it off within six months, and left it open. My credit score is considered "good". I am currently a SAHM so no income for me.

We need a credit card, for emergencies and things like renting cars. We also travel often, internationally, and will be moving back overseas next year.

I want to find a credit card that we can get approved for that we can use for our everyday purchases and pay off each month. Ideally something with cash back or miles rewards.

So my question is - any card recs? Should DH apply (with no credit history but a job) or should I (with a good credit history but no job)? Is there anything else we should be doing to build good credit for both of us?