You can ship a long gun, through Fed-Ex or UPS, but you have to take the gun to one of their hubs. A UPS Store won't do it. You should check with the receiving FFL first though, because some of them won't accept anything from an individual. That's not in the law; it's their personal rule.

Only an FFL or their representative can ship any gun through the USPS. Some of their counter people don't know this, and get jumpy when you tell them it's a pistol you're shipping.

Handguns have to be shipped FFL to FFL.

For FTF sales, I do the same as what Scott said. No paperwork at all. I just make reasonably sure they're a Missouri resident and already own guns before selling to them.

Ammo is a bit more involved, because of paperwork and stickers (ORM-D I think), but firearms are easy.