Whats a "high limit"??? 10K?? 20K?? 100K?? Some lenders have limits on some of their products so your definition of high limit wouold help. AMEX Gold or Platinum with membership rewards is one to consider but obviously you have to PIF every month (which you should be doing anyway. Chase gives fairly large limits out of the gate. If your fly Continental or United, their Presidential Plus is a great one. My initial limit was 22K.
I believe Travelocity Amex give out the best reward in term of discount%. You could get 10% cashback for future travel purchase and 4% back on select category for the 39$ AF version. Your credit line for barclay card will be determine by other credit lines showing on your credit report. If you have some high limit cards already, you could recon to match those TLs. If you have only toys, expect to get another toy and it could be as low as $500. Their co-brand cards usually have high to very high apr. I think reward and apr are two things that will unlikely go together. You need to sacrifice one for another. I have FIA fidelity amex from BOA with 2% back on everything and apr is somewhat OK at 13.99%. You can't really expect great reward card with 6.99% apr.