... would be the most difficult or almost impossible for hackers to break (hack) into, or to intercept my emails.
eMail can be intercepted. It's part of the protocol. Whether it's pop, smtp, imap, exchange, Lotus Notes or web based eMail will never be completely secure
or reliable.
What do you want to send securely?
You can personally secure the content of any mail with encryption such as PGP, this will not secure who you have communicated with, from what server, when. It will not stop people intercepting your communication, but will make it extremely difficult to determine exactly what was communicated. Make sure the recipient is using a secure mail client too. You can do that when you are exchanging public keys for all your following correspondence.
If you want to secure access to a web mail account, make sure you use strong passwords (as Ron said) but also make sure you only ever log in using secure http connection. (check the url begins
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Do not allow any page which presents a message from your browser that "some elements on this secure page are not secured" or similar, and never tick the box which says "don't tell me about this in future" or how ever your browser chooses to word it.
If you do not wish anyone to know who you are communicating with, or when,
do not use eMail for your private communication.
The eMail standard was always intended for public, non-confidential correspondence. Any attempt to completely secure it would disconnect that new protocol from all other eMail users. Why do you think Banks make such a big thing about "never sending you eMail".
You can secure either end, but the bit in the middle, where your eMail is going to the other person, can only be secured by forcing both clients (yours and the recipients) off the internet and on to a private network. (Internal Exchange server between two people both locally connected to the same LAN, for example, is "secure" eMail)
In short, you are much better off hosting a shared folder from your computer over an SSL tunnel which they have to log in to.