If you must have the Internet onboard - or even just email, then its best to use a laptop.
If you really want to use your iPhone do it like this...
Get an Internet acct onboard and log into it with wi-fi through the phone browser. You will have to go to a website and log into the network EVERYTIME you want to check your mail.
But once you are logged in your phone should be able to download your email through the wifi.
As stated, even if you do this it is extremely important that you make sure data roaming is turned off at all times. otherwise, just a few emails can easily cost you $20+ if they contain pictures. The usual cost is about $5 MB (for phone data roaming).