If Panama is like the several CA countries I visit, getting a phone and a prepaid SIM will take minutes. You will likely have to get a new SIM in CR but a basic unlocked phone for calls and messages will be available for next to nothing.
Smartphone with a prepaid data plan not much more work but of course more money.
Since CDMA and GSM are two totally different things hardware wise I doubt you can switch an iPhone to GSM if it already is not using a SIM. Although apparently the iPhone 5 for Verizon has a working GSM SIM slot. I would not count on that vs. buying a burner. There are basic smart phones in Managua for $40 or $50 brand new but locked as an example.
Just make sure you check the GSM frequency in Panama vs. CR or to be totally sure get a quad frequency phone which most or many are.
You may find that one of the carriers will cover both countries (like Claro in Nicaragua will work in CR) but don't count on it. I have a Movistar locked phone for Movistar and a few unlocked GSM phones since the Movistar phone doesn't work even with Movistar in San Jose for some reason. If you buy one in Panama the service provider might not exist in Costa Rica. Make sure it is clear when buying you intend to use it in both countries.