Carry at least two cards on your trip to Mexico, preferably connected with Visa or Mastercard. If you just take an American Express card, you won't get to use it in many places. Think no foreign transaction fees.
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Bringing a small amount of cash in the local currency with you is always a good idea. This could help in any unforeseen emergencies where you may not be able to use your credit or debit card.
Follow the 25% rule regardless of how many days you will be in Mexico. For example, if your total budget for a seven-day vacation is $1500USD, you should bring a total of $375USD or $7,000 MXN. This totals about $50USD in cash per day.
It's recommended that you buy pesos before you land in Mexico, just in case you need the cash. According to this USA Today article, the most economical way to do this is to buy pesos from your bank in the U.S. Most banks will do this for free, especially if you're not withdrawing a significant amount of money.
The golden rule of credit card usage is to do everything you can to pay off your entire balance each month. If you can do this, you won't be charged any interest. You'll be enjoying free credit and all the other benefits your card offers. Be sure to always make at least the minimum payment on your card.
For traveling (even on a backpacker budget) it is perhaps better to consider what 500 pesos (or $25 will buy). That is enough to rent a car for a way (minus non-specified expenses). It is also enough for dormitory accommodation in some of the cheapest hostels in Mexico City for two nights (around $8 per night).