Just turn the data connection back on for the times you want to use it, and then turn it off when you're done. WiFi still works when the data is turned off as well.
It may just be a particular app I have that tries to use the data connection when I have stuff set for things not to, but technically, all you should have to do is turn off sync and turn off background data. Then your data connection is still active, but it won't be running anything you don't know about. You'd be able to use Gmail or chat whenever you want without turning the entire data connection on and off. Give it a shot before leaving to test it out to see how it works for you. It should work just fine.
One advantage to a prepaid SIM is not really having to worry about the data access. They're relatively cheap, especially compared to the rates Verizon charges for you to roam internationally with the pre-installed SIM. If you're going to use the phone with the SIM card Verizon has in there, you're going to pay quite a bit for any data usage. It's simply not worth it unless you've got the cash to blow. I normally pick up a prepaid SIM for a few dollars, and I'm set. A prepaid SIM won't work so well in South Korea though (I used to live there and still travel there, and their cellular restrictions are ridiculous).
Calling cards are great for using landlines or a local cell phone, but using them in conjunction with paying for international roaming (if you use your phone with the pre-installed Verizon SIM card) is far more expensive than a prepaid SIM. If I need to call out of the country on the prepaid SIM, I just pull up Skype mobile. Buying minutes through Skype is typically cheaper than a phone card (at least in the places I've been).