Simple as this: you want push mail on your android phone with one of your “regular” accounts (pop mail), and as you know that can be pretty tricky (at best). But, fear not! Google of course got a solution for that.
You simply add the accounts (up to 5) you want to use into gmail (use computer), and you add pop3 settings and such and if you want to: you can even add settings for sending mail via gmail. And since Gmail is push, you get your mail more or less instantly!