Just follow the
set-up of the iPhone's mail client for using Google Mail and make sure
IMAP is enabled in your Gmail account's settings. Although I simply did it via the specific "Gmail" option on the iPhone, rather than following Google's instructions in the first link - apparently that changes how messages are archived & deleted.
No need for WiFi.
Google Sync doesn't do OTA sync yet for email, but hopefully that will be something Google will change...