POP and IMAP are the protocols you will need to consider for your client.
POP - Post Office Protocol - will get all the email from your server and load it to client.
IMAP - Internet Message Access Protocol - allows user to setup an email account as long as you have username and password.
let's say, you have 1 Ipad, 1 Samsung Galaxy, 1 Android Phone, 1 Laptop and 1 Desktop - IMAP is away to go. Because the mails are always on the server that enables the user to configure on multiple devices.
if you already have a domain and you want your gmail account to forward to your own email domain, check out link below:
Forward mail to another account