When adding an additional email account to your email client (Microsoft Outlook or similar), the "outgoing" setting should be the same as for you existing email accounts.
For most people, the outgoing settings are those for the Internet Service Provider's SMTP server. The SMTP server names usually start with "smtp" or "relay":
BRAINBOX clients: please do not attempt to send email via your (BRAINBOX) website's mailserver.
Most email clients (such as Microsoft Outlook) allow you to set up a number of "profiles", each with a different "from" address. So when you write an email, you can choose (for example) to send from your personal address or your business address.
Although the email system typically doesn't test that "from" addresses exist (though they may test that the associated domain name exists), make sure that "from" address is a working email address to which you have access.
This last point is important is you use more than one email address.