Lead source / channel capturing using original fields

Hi,

We are using the original referrer, referrer and querystring to capture the source (we call it channel) of the lead's first conversion but the problem is that the original referrer and referrer are not necessarily connected to the first conversion. For example there might be cases where a lead came to our website from an ad and never converted. His original referrer will say that he came from an ad but the conversion may be actually direct or any other source. Which fields I can use to determine the source of the first conversion and the source of the first time the lead visited our website? Any best practices?

Thank you.