In general, I think it's silly that gun records are necessary. It's a tool like a chainsaw, hammer, or knife and none of these are registered.
However, given todays climate of gun regulations, I think you're a fool if you don't make some record of the transaction. A handwritten or typed bill of sale/transfer identifying the parties, date, serial number, description, drivers license and address and a statement saying both parties legally can sell/buy/possess said weapon is prudent.
Here are some scary scenarios if you fail to make a record. On Jan 1, you buy a gun from Joe. The following June Joe is burgled and "forgets" he sold his pistol to you. Nine years later you use that pistol in a legitimate self defensive shooting and that pistol shows up as reported stolen.... Now, if you can't prove where and when you got it, you've got some serious headache and heartache ahead.
Alternately, Joe could maliciously report it stolen.
Joe could use it in a Christmas shooting spree and sell it to you. Now you've got a weapon used in illegal homicides and no record of who or when or where you bought it.
OR, You sell your pistol or rifle to Joe. Joe buys it intending to commit a murder and dump the weapon. Weapon turns up, ballistics and prints match your weapon and you. You've got some questions to answer and no good answers... "Well, officer, I sold it to this guy a year ago. I don't remember his name but he drove a white car and was wearing a red shirt..."
You get the idea.
In all of my transactions a bill of sale is prudent and will likely scare off the unscrupulous. I check their ID to make sure the are the right identity, age, and also if they are a voter. One tip, if they are not a voter, chances are they might be a felon and it's illegal to sell to that person.