A "straw purchase" can only occur when a person is getting a gun on behalf of another person from a dealer and lying that they are the actual purchaser on question one of the form 4473. This does not apply if the person is buying the firearm legitimately as a "gift" for another person from the dealer though. A straw purchase cannot occur as a private sale between two residents of the same state.
If you are concerned the buyer may be a prohibited person or buying it for other than good intentions I would suggest transferring the firearm thru a licensed dealer (FFL) in your area. Most will do it for $20 or so (that's what I charge). That takes it out of your name and the buyer will have a background check done to show they can legally own the firearm. Some buyers and seller split the fee.
Of course then the buyer would have to be 21 for a handgun to come from a dealer or 18 for a long gun. I know the laws don't always make sense but they are what they are. Hope this helps some. chig