How do I pay my @me.com mail account in advance?

There is no charge for your email account as such. The only charge is if you have extended the storage from the free 5GB. This will automatically renew unless stopped, so it's just a question of making sure that Apple have the details of a valid credit card.

If your credit card expires and there is a renewal due before you can do something about it then the renewal will obviously fail and the storage will revert to 5GB: this could lose you data if you have more than 5GB in there. All this applies only to the storage: the email will keep working anyway (unless there isn't room in the account for incoming messages).