Most of the world uses the GSM phone standard, but Verizon and most other carriers in the USA use the CDMA standard. You cannot use a phone for one on the other. You might find
useful. Most of the islands supports GSM.
If you want a US GSM phone that you can use in other countries, get one from T-Mobile or AT&T, but make sure it is unlocked
or that you can unlock it yourself so you can use it with other phone companies' systems. You'll have to investigate to see what AT&T or T-Mobile offers in terms of family plans. I'm a Verizon subscriber and have no idea.