I'd start with local Armslist and go from there, you may get out of state inquiries as well... Gunbroker involves additional fees and selling requirements that may be more of a pain if you don't do a lot of selling-buying.
You can sell the firearm via whatever mechanism chosen and ship it directly to an FFL in the buyer's state where they would complete a background check and comply with their local state requirements for a legal transfer. Some FFL's will only accept firearm shipment from other FFL's so, while not required under law, so you may need to work with a local FFL to ship the firearm. You'd need to look at the particulars with a shipping carrier (the USPS will NOT ship firearms, UPS or Fedex only) as to how an item needs to be described/declared for shipment.
https://www.atf.gov/content/firearms-fr ... ed-personsQ: May a nonlicensee ship a firearm by common or contract carrier?
A nonlicensee may ship a firearm by a common or contract carrier to a resident of his or her own State or to a licensee in any State. A common or contract carrier must be used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm.
[18 U.S.C. 922(a)(2)(A), 922(a) (3), 922(a)(5) and 922(e), 27 CFR 478.31 and 478.30]