cell phone in Mexico

Motorola phones are about as close to "universal" as you can get. Even the MotoE series has quad band (CDMA and GSM capabilities).
Moto
Either buy from Motorola direct, or ensure you buy an unlocked phone from Amazon or whoever. If you buy from Verizon, ATT or another cell provider they will have locked the phone to their service before you receive it.

Here is a link to a current discussion on the Zihuatanejo Message Board that may also be helpful to you: http://www.zihuatanejo.net/tablero/thread/137752.html

IF you had an unlocked cell phone from the US, or anywhere, you could just buy a SIM card for 26p, put money on it and be set.

Yes, you can buy "plans" or normal, but either way, it's cheap. We don't call the US or Canada (or call much at all) so we just put 100p per month on the phone. After 30 days, you need to put on more money to keep it active. 100p gives you 30 days, and the balance rolls over. Without money being added, you keep the number for 1 year, just add money and you are done.

In February, he had to fly to the US for 2 days. He took the phone, but wanted to call me. We went to TelCel and asked for the cheapest phone. Out the door, just under $18 US we got a phone for me, SIM card, and 10 days of unlimited calling to the US and Canada. Included in that price was 5 days of unlimited everything for his phone. It's cheap.

Don't buy the card on Amazon. We made our living (and bought our house here in Zihuatanejo with the proceeds) on eBay. Wish I had known that I could buy SIM cards here for 26p and turn them for huge money on eBay and Amazon!

A number of people, including Tequila, have found that the TelMex phones and their service are so inexpensive and reliable that even though they are based outside of Mexico, they use the Mexico service. Plans are explained on the TelMex website and payment can be done there too.

Don't know about GSM vs CDMA, but I've not heard of any cell phone not working here that isn't just wifi.

You need an unlocked GSM phone. You can get a SIM card to join the Telcel Amigos sin limites plan (150 pesos for unlimited calls/texts to and from Mexico/USA/Canada, unlimited Facebook/Messenger/Whatsapp/Instagram while in Mexico, and about 1GB of data, at most big box stores in Mexico (Walmert, Chedraui, La Comer,etc.). You can recharge your account at all OXXO and thousands of little stores, or on line (website or Telcel app).