Well since you are looking to mainly use it in the event someone doesn't accept AMEX there is a chance they will not accept Visa or Discover either so I'd stick with Mastercard for 99.99% acceptance worldwide. I would also stick with a no foreign transaction fee card since if you ever plan to travel you won't use your AMEX due to lack of acceptance and foreign transaction fees. So a no foreign transaction fee Mastercard..

The choice that would come to my mind would be the Chase Sapphire Preferred Mastercard with a 40,000 point ($400+) sign up bonus although after the first year you would have to justify the $95 AF, which isn't hard to do if you use it for the 2% food/travel. This card is 15% with no 0% intro, but I'm sure the sign-up bonus would offset any interest charge.

Don't forget, you have to go through Mastercard.com to get the Mastercard version CSP application.

Wallet: JP Morgan Select Visa Signature $9000 | Chase Sapphire Preferred $5000 | Chase Freedom Visa $2000 | Barclaycard Visa $3000 | Discover More $1500 | Capital One Platinum Mastercard $750 | Bank of America Cash Rewards Visa $500 | Walmart Store $950 | Amazon Store $5000 | AMEX Zync (AU) NPSL | Chase Total Checking | RIP: First Premier Mastercard

We can't said anything since we don't know your credit file........

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Starting Score: 560
Current Score: 748 Wishlist: CSP, Simply Cash, SPG, BOLD, INK, United MP,
Goal Score: 800

Walmart: 10k | Usaa: 8k | BCE: 3k | Amex Green: NSPL | Cap: 2k | Disco: 3.4k | ORchar: 0.4k

If you want to finance a computer, and want to go Mac, you can do the Apple Financing Visa card from Barclays. They run 0% for 12 months all of the time. Pretty generous with CL, too.

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Starting Score: TU TransRisk 532| EQ FICO 635|EX Plus 612
Current Score: TU TransRisk 590|EQ FICO 681|EX FAKO 676|Vantage 684 as of June 10, 2013
Goal Score: 750-800 across the board

Take the FICO Fitness Challenge

I'd say Chase Sapphire Preferred or Capital One Venture

AmEx PRG (NPSL) | AmEx Costco ($8,200) | AmEx Delta Gold ($7,500) | Chase United Explorer ($10,000) | Chase Sapphire Preferred ($7,500) | Chase Freedom ($8,200) | Discover it ($3,000) | Capital One Platinum ($2,500) | GE Lowes ($3,000) | GE Walmart ($2,800) | GE Amazon ($2,250)
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Homeowner since 05/29/13

You could look at the Chase Freedom card.  It has 15 months of 0% and is a solid cashback card.  Since the Amex you have is a Zync, I assume you don't travel frequently.  If you do, you should take a look at the Sapphire Preferred.  It doesn't have a 0% offer, but even if you do have to carry a balance, the signup bonus will make up for that.  Also, all of Capitol One's products waive forex fees.