Here is what works for me.
Get a mail account called domain\sqlmail (insert whatever you want).
Make sure that same account has an exchange account and/or any mail server your company uses.
Have that same account be a local admin on your SQL Server that will be using SQL Mail.
Have that same account run the services for BOTH MSSQL and the SQL Server Agent.
Make sure Outlook is installed on that server.
Make sure your profile works and you can send and receive mail (with Outlook program) while logged into the SQL Server with that same account.
Then hook that profile up in the properties of SQLMail.