In any firearm transaction, I want some reasonable assurance from a buyer/seller that he/she is a legal buyer/seller.
When buying a firearm, I prefer getting a bill of sale, but I don't necessarily demand it. Depends on the circumstances.
When selling, I'll give a bill of sale if the buyer wants it.
I don't record any information on who I sell a firearm to, unless there's a paper trail on the firearm to me.