For less battery usage better option is infinity awaiting for new email. One require: email server must has that functionality (gmail has).

Fetchmail do it perfect (from easy debian debian_jessie1sulu_armhf.img.lzma from http://qole.org/files/)

in fetchmailrc file, enable two function:
keep
idle

It works like SMS. Fetchmail connect to server. It keeps connection and idle. When email server gets new message then it inform fetchmail that is new message and fetchmail pulls it immediately. No power waste for constantly sync and it's the fastest method as can be.