If you are only backing up locally, with no database agents, then Local System Account will work fine.
if you also backup remote servers or workstations, or connect to SQL or Exchange, Veritas recommends that you create an account for BackupExec and give it domain admin rights. If you don't want to do that, you can (in the backup selection pane) right click on a share or drive, select "Attach As" and give it an account with rights to the resource. And no, that user does not have to be logged in for the backup to succeed.