If you're looking for a new "throwaway" card, I recommend Capital One. I've had one particular Cap1 card reported lost twice bc of fraudulent charges and all Cap1 did is remove the fraudulent charges and send me a new card number. No new account was ever reported either time. I misplaced my Barclays card last month and they promptly sent a new card with a new number. They only updated the card number on my credit reports.
I'll second the cap1 recommendation even though it isn't the most "prestigious" card out there. Their fraud detection is very good... they have usually detected fraud even before I've become aware of it and shut down the card.
I do have the Quicksilver, which is going to be my gas card from now on. I'm giving up a little bit of rewards, but not dealing the hassle of BB&T as well as their $25 minimum to redeem is worth it, IMO. I also have setup my Apple Card to work with the Exxon app, so I can pay securely there and get 3% cash back.