First off, I am going to make the assumption that you are shipping to an FFL holder. If not you can not legally ship them, unless you are shipping to yourself. With that being said...
If you are a non FFL you can send long guns through the USPS. I use priority mail. Just make sure you get insurance. The Delivery Confirmation is worthless, IMHO as it only shows when a package has arrived, nothing along the way.
For rates you can go to usps.com and clinck on calculate postage.
If you are an FFL holder you can mail handguns. Enough said.
You will have to fill paperwork out at the post office. Simply tell them you have an unloaded firearm that you need to ship to an FFL holder. It doesn't hurt to have a copy of the FFL with you, but I don't believe that it is required.
FEDEX/UPS/DHL have all become a real pain in the ass to deal with when it comes to firearms. I have found that the policies vary from office to office. The retail store (formerly Mail Boxes etc and Kinkos, now UPS Store/FEDEX Store) will not accept firearms of any kind. You must go to the actual UPS site or FEDEX site. IF they will ship, they will most likely require that you ship it overnight express (most expensive service) They will require that you have an FFL in hand, either yours or the one the gun is going to. They very well may demand to inspect the gun to ensure that it is unloaded. Again this is all based on the premise that you are dealing with one of the sites that will take a firearm from a non-FFL holder, it varies from location to location.
What are you sending?