If you are talking about 1K/year, it probably does not matter if it is a 2% or 0% cashback - it is only $20 difference.

On the other hand you may want to look for a visa/MC with a 5% category. For example, the PenFed visa gives you 5% on gas and 1% on everything else; Citi Forward visa gives you 5% on dining and 1% on everything else; there are other similar choices out there if you want to remember which card to pull out for a certain category.

Another thought will be getting a fee free World MC or Signature Visa for the benefits.