If you're going to have an email account it may as well be a reasonable size. If you want huge you'd go for an Exchange account like the ones we offer with our Microsoft Office 365 product but even a regular email account shouldn't fill up in a day.
Our Aztec 365 accounts are 2Gb in size a standard and you can connect to them with either IMAP or POP3. And they are all accessible by either your email program on your computer, tablet or phone and also via webmail.
So the only question is, how many do you need?