How can I get Apple Mail to pick the correct From: address?
The box below the Subject line is called the Mail Box. 

It is like the Post office name.

It is used to select from which email account you want to send it.

The first box is From, the second is the Account from which to be send.

You can change it here:



When you open new email window you ca also change the settings here:

For the From field, and choose which account to use.