Send an auto-response emails from the lead owner’s email when a new lead is created

I would suggest to use workflow rule.

Setup->Build->Create->Workflow & Approvals -> Workflow rules->New rule-> choose Lead object.

Then, assuming you don’t need to do anything else I would select “evalute the rule when the record is created”. This will only trigger the rule once for that record. From there, you can go figure the selection criteria to trigger an email to the record owner that Web2Lead assigned to the lead. The wizard will walk you through but come back with questions if any.