Hi,
You welcome email will autimaticly be send when a user subscribes to your list via the frontend. In case you use double opt-in it will be send after the user has confirmed the subscription.
In v9 you can send an specific email to a specific user using segments. Though you can use segments in your email sending process, in this case I would recommend to use a mass action. Select "Add an email to the queue" on the Actions tab and set a filter that matches your user on the Action targets tab.
You'll find the mass actions on the Automation menu item. Both segments and Automations are part of the Enterprise version.