I would look into the Wyndham card first. It's a VISA, so will be usable at Costco. If she stays at those properties then the 2 points earned on all spend leads to some nice rewards. You use 3,000 points for a significant room rate reduction at most properties, so as a reward card, it aligns very well with some of her travel spend. The no AF card means she can accumulate points without extra costs.
Barclay is also the kind of bank where they would like to be the first bank. Sure, the AU and 6 months history may be a barrier, but she won't really know what Barclays thinks until she applies. Since it is (in my opinion) the card that most easily aligns with her spend, it is worth a HP to find out.
Then, if Barclays says no, and even if Barclays says yes, I would have her just apply for the Capital One Quicksilver. 1.5% in bullet proof cash back, no AF, no FTF (if she travels to Canada for example), just a no worry, good to have card.
And I'd ignore all the other cards. Seriously. One can get too refined in the analysis, and at the end of the day, with $15k total income, the earnings on spend are just not going to vary significantly with any other cards.
In my recommendation, it's either Barclay Wyndham, or Capital One Quicksilver, or both, and no others. Simple.
