Clay,
Sadly, any email which is sent to an email server (in the US and most other countries) is retained (by law...) forever.
"deleting" from your online mailbox DOES NOT delete it from the server, it just marks it as "do not display". Again, that is in most countries, but not all.
You may encrypt it before you send it, which is some (small) protection, but any encryption CAN be broken, given enough computing power applied to it. That is why using higher levels of encryption (harder and more time consuming to crack) is the only way to go. At least 2048 bit encryption keys, with 4096 bit recommended.
I too received the notice from Yahoo about the latest large breach (1 billion accounts had information stolen). This is the SECOND breach on their servers, which means they have (had?) more than one hole in their security screen.
SO, that is why I looked fro an email provider that offered the best security (hardware, software and policy) AND which was located in a country which does not subscribe to the the email retention policy. FYI it is Switzerland.
My other criteria was that it be free, which eliminated several servers from my list.
PM me if you want more information about this. Let's not make it easy for anyone who wants to breach our secure comms setup.
I have heard it said (hearsay) that one way to increase security is to have EVERYONE encrypt their comms, hence nobody will "stand out" as something unusual.
Sadly, again, we are a long way from that solution, but more people are waking up to the problem.
Do you remember the song "Who do you trust?". It seems apropos here.