Customizing trust level promotion messages for new users is a great overview of the automated messages that are sent to users. Maybe customizing those already fulfills your needs, as the TL1 promotion message is sent after about 10 minutes of reading by default.
Otherwise, you can use the automation plugin. It offers a script to send a personal message, for example, when a user joins a group. After registration, every user is added to the trust_level_0 group. The script also allows you to select a sender and a delay.
Depending on how you configure the default email messages level, users will always receive an email when they receive a message. This would also affect the welcome message you send.