Best credit card or someone with little credit history

[ENL]

So my husband doesn't have much of a credit history.  He doesn't have any credit cards of his own (though he has been added on as an additional cardholder for a couple of mine) and the mortgage is in my name since I bought it before getting married to him. 

We just applied for a card for him and they denied him due to: "Few revolving accounts opened long enough to establish credit history" and "Not enough accounts opened long enough to establish a credit history."  Despite this, the rejection letter also states that they determined his credit score was 780?  Not sure how that high a score is possible with the lack of history they mention, unless they printed my credit score for some reason (mine is also in the high 700s).
 
Anyway, I'd like to get him started with a credit card in just his name so he can start to build credit and not be as reliant on me for credit in the future.  Does anyone have any recommendations for a card or a good place to do the research myself?

So we definitely want no annual fees or other sneaky ways to grab our money.

The ability to do a balance rollover from another card we share would also be fantastic, but not a requirement.  We have a balance of about $5,000 on a Chase card that we are working on paying off (should be within a year).  I would be great to roll over to a card with a 0% introductory APR and a low/non-existent rollover charge.   I know I could just roll this over to a card in my name if necessary (and I would be accepted for pretty much any card I wanted), but I hate to open up yet another line of credit.

Rewards/cash back is not a factor.

[JLee]

Chase Slate is running 0% for 15 months, but I am not sure how fussy they would be on credit history.

[ENL]

That's actually the card he was applying for when he was denied.

[JetBlast]

I'd look into the offerings at whatever bank he has his checking and/or savings accounts with. They may extend a lower limit card to try and keep his business.

[SF Semi-Mustache]

I'd look into the offerings at whatever bank he has his checking and/or savings accounts with. They may extend a lower limit card to try and keep his business.

+1.  I started out with a credit card from my credit union, and after a year I was approved for a "normal" Citi rewards card. 

[johnny847]

There's a list of "starter" credit cards here http://www.doctorofcredit.com/starter-credit-cards-best-cards-for-people-with-no-credit-history/

If your husband doesn't get approved for these, then he may just have to get a secured credit card.

[GizmoTX]

When our son was 17, I took him to our local bank (Wells Fargo) to open an affiliated Visa credit card, no annual fee, cash rewards, initial limit of $500. He already had a student checking account there, & we had an account & history there as well. DS was primary on the card, I was secondary. He used it primarily for gas purchases & paid it off in full every month, earning some cash refunds in the process. After two years, the bank had raised his credit limit to 1.5K & his credit score was 780, even though he's a full time student working summers. Last spring he was able to get a Capital One Quicksilver card on his own with a $3K limit.

Bottom line: try your bank first for a starter card, start small, never miss a payment.

I wouldn't muddle trying to establish credit with a rollover, which usually costs 3% up front & can be tricky.

[ENL]

I wouldn't muddle trying to establish credit with a rollover, which usually costs 3% up front & can be tricky.

There is no way I would do a rollover unless there were no fees associated with it.