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.