I fly pretty frequently from North Florida to Washington, DC. Usually, I take Southwest, although I have flown on Delta when presented with a total lack of choice. These are my personal experiences:
Both Southwest and Delta list their firearm requirements on the web. Print out a copy and bring it with you.
Federal regulations state that you must transport your firearms in a locked hard case, with an affadavit (usually a tag) stating that the firearm is unloaded. There must be no external markings that indicate a firearm is contained inside.
Southwest currently lets you fly with 8 lbs of ammo, Delta with 11. Flying out of North Florida, no one has ever weighed it. Flying out of DC, it gets weighed every time. Both Delta and Southwest allow ammo to be locked inside the pistol or rifle case, provided it is in it's "original container" or other approved container (NOT IN THE MAGAZINE).
I have never had a problem checking a firearm. I am always polite, and allow the attendant to direct the inspection. I sign the affadavit, throw it in the case, lock it all up, and off it goes. Since post 9/11, only firearms cases can be locked, so I often throw other valuables in the case.
As to cases, Pelicans are indestructable. However, you stated that you wanted a case that looks good, too. I highly recommend Kalispel aluminum cases. I have a large rifle case and a pistol/utility case. They are beautiful, secure, and built like a tank. They are also priced competitively with Pelican.
Don't sweat flying with your firearm. Be polite, be informed, and you'll have no problems.