In order to ensure that BOTH my phone and home PC get them, do I need to leave the setting at the server to leave them there until I manually delete them from the server?
I hope that made sense.
Not really. AFIK, unless you are running your own mail server, you can't change the settings on the server that your ISP runs. If your place of work runs its own mail server, it can change settings on that server.
You can only change the settings on your own mail client -- that is, the mail program you run on your PC and the mail program you run on the phone.
As I understand what you want to do, you want all e-mail to go to both your PC and your phone. To ensure that happens, neither mail program can allow the mail server to delete a message when it's downloaded.
Takeshi and KMF pretty much told you what settings you need to use in K9.
For example, in the Mozilla Thunderbird program, you'd want to set
(X) Leave messages on server
to
(X) Until I delete them.
Then you have to decide if you want to delete messages ONLY on your PC or ONLY on your phone. Of course if you know you don't want to save a message, you'll have to delete it both places to clear it from the mail program, although the first delete will clear it from the server.
If you're sure you'll know when a message has been downloaded by both mail programs, you can delete it on either. But how can you, really? However, if you're sure you don't want to save a message, you can delete it on either program, and it won't matter if the other program doesn't download it.