If it's a rifle or shotgun, you can legally ship via Post Office. I hand over a copy of the receiving FFL to the postal clerk. But your local PO folks might not be aware of the laws. I've done it dozens of times. UPS doesn't require any markings on the package. I don't have a FedEx nearby, so ignorant there.
It's actually legal (to my knowledge, but you should check your local laws, I'm in SC) to ship without using an FFL within a state (but check).
Most folks I know use postal money orders. Fairly cheap, and secure. But, if it happens to get lost in the mail, it's 90 days before the money can be recouped. A cashier's check also is as safe as the money order.
Using PayPal for a gun purchase, should they discover this, will result in your PayPal being closed. I've been told this, but not personal experience. I don't use PayPal.
Once you've done this a couple times, it becomes a snap. Best of luck with your transaction.