Simple solution: get an Outlook.com account and get it to collect all your Gmail. Use Gmail forwarding to forward all incoming emails to your Outlook.com account, and bcc copies of outgoing mail. You now have an off-site backup.

Install a desktop client and download all your Gmail using IMAP. You now have an on-site backup, and you can use your client to send emails via Outlook.com.

It's not hard. Anybody could do this.