I have only flown Houston, TX to Las Vegas, NV and back a couple times. Check with the airline for what they want to see in terms of packaging and inform yourself of the respective state laws in PA and wherever you go.
This has worked for me, YMMV: slide locked back, lock through the action or barrel. Gun into lockable Pelican case. Ammo, Continental allows up to 11 lbs (stupid limit - who in the world shoots less than 11lbs per trip???), either in original factory box or a cardboard box in which the ammo is securely packed.

I usually take a couple 500rd bullet boxes, put the ammo in a zip lock bag, ammo goes in box, paper or other stuffing material goes on top to fill the box and compress the ammo. Then I duct tape the box tight so there is no rattling when you shake the box with ammo. Ammo goes in suitcase.

At the time of check in, I tell the person that I am declaring a firearm. They tell me where to wait for friendly TSA assistance. The TSA person will direct me (what to do, where to stand, whether I or they handle the firearm). Once the check is done, I lock the outside of the Pelican case with the other two locks and put my handgun IN THE SUITCASE. Nobody then knows what's in the suitcase and it's less likely that a large suitcase gets lost than a small guncase with a "firearm" or other label.

I hope this helps a little. Keep in mind that your local laws may be different. The airlines usually have a sheet available online that you can print off. Take it with you in case you are dealing with an ignoramus at the airport - that way you'll have it black on white.

All in all, it's no big deal. Safe travels!