How To Setup Ubuntu Server to Send Emails

I have several domains hosted by GoDaddy. I used to have a server setup with VestaCP and it was emailing from HBF-SERVER.example.com using an MTA and somehow configured itself to do it without me doing anything.

I have a server that I want to have the ability to send emails out from a specific email domain. All my emails go out from a domain designated for emails. Is there a way I can set my server to send out from the domain by default? I’d prefer to keep my email with GoDaddy. I am not looking to set up a private server.

I have a specific email address webmaster@example.com that I use for sendemail command line situations. Is it possible to configure the server to relay all emails through webmaster@example.com?

Any help would be appreciative.