There are probably others in this community who are better able to respond to your question than I, but I'll start out. Although there have been several discussions of mobile/cell phone use here, most concern places outside the US. As many people have mentioned, cell phone service in the US lags way behind that elsewhere, particularly Europe and parts of Asia. Here are some factors to consider.
First, most plans, though not all, involve long-term contracts, usually two years. There are some pre-paid plans which don't require them, however.
Tracfone is one, although one poster didn't recommend it.
T-mobile is another and probably better option.
Here's a new one I just found, Net10, which consumer advocate Clark Howard now recommends. If you choose a phone, this may indeed be your best option. Most international calls are only 15¢/minute.
However, you'd still confront another issue. All phones don't work everywhere because of different technologies and geography. We had to change our service after a move because our existing phone wouldn't work at our current home.
You'd have more flexibility, though, with a phone card. In the past, that's what Clark Howard has recommended.
Pennytalk is one which seems particularly reasonable. You may be able to sign up online and get a number to use without actually having a card in hand.
Good luck!
Ann