Verizon Wireless in Playa del Carmen, Mexico?

I will be traveling to Playa del Carmen later this week. I have a Verizon iPhone and as far as I understand, I should be able to use it without a problem there. I believe the rates are .99/minute to call, .50 to send text messages and .05 to receive text messages. My only concern is if I'm not using my phone, should I have it turned off? Or can I leave it turned on and just make sure I don't have any apps turned on that automatically try to connect to a network? (my gmail account for example). I don't want to come home with a huge bill. Thanks!