To be honest, at least for me, the best welcome email is no email at all. It clutters my inbox and I really don't crave the feeling of being your very much appreciated customer. It usually annoys me more than it helps.
If I have a problem and contact you, then your personal and prompt response is an entirely different matter. Then it is appreciated.
I like a confirmation email to let me know that my signup to their service really did go swimmingly, but I don't care whether it's by a robot or a human, because I don't read them. The email title "You successfully signed up for Facebook!" gets the point of the message through well enough.
Yes, I understand your point. For some (maybe in your case, all?) products, it can be annoying. But with early-stage products, that first touch-point is critical, and I believe that you want to make your message as authentic as possible.
If you've got a working, post PM-fit product, I think you'd be using a whole different set of tactics.
If I have a problem and contact you, then your personal and prompt response is an entirely different matter. Then it is appreciated.