FFL transfer requires your ID to take the rifle in and then buyer's ID and Form 4473 on their books. Send your ID to the FFL. Document the transfer on your end.
PayPal and other online payment companies don't allow purchases for firearms, so if the buyer puts in the description that it is for a gun it can get flagged and then they will hold your money, maybe never get it. If the buyer is good to go with good rep on forums, that's usually enough for me to accept PP.
I don't know any specifics about other states or anything, but that has been my process. If you have questions, have the buyer confirm with the FFL and send email to FFL to document.
I have shipped long guns by USPS and UPS. Pistols (AR 15 included) cannot be sent by USPS, they must go UPS or Fedex. If you try to ship through UPS store and disclose contents as you should, they will likely refuse. I have sent through my local shipping store, they just take the box cause I preprint labels. If you have a UPS hub, you can take the rifle there with a copy of the FFL and they should accept it.
In the end USPS is the easiest. I think you can even go online, enter dimensions, and then print your label. I would go to local shipping stores that do USPS and ship it priority to the FFL. Best practice is to require a signature.
Don't ship in a box that has markings indicating it is a firearm.