The wait time varies with the time of day and the airport. The longest I've had to deal with TSA was about 30 minutes in Reno NV. They insisted on swabbing the the interior of the case for explosives.
Omaha is pretty good. No one got excited when I opened up a case full of evil black AR's and mags.
A few folks in line asked if I was a LEO. I said, "Nope."
I use a good lock. I don't think it has to be a TSA lock. I've never used a TSA lock. YOU have to be the keyholder though. Usually they make you wait around until the case clears the xray unit (depending on the airport.) They have you unlock it if there's a problem of some kind. Otherwise, they cut the lock.
The ATF takes firearms theft on the airlines pretty seriously. Theft does occur but it's rare. Firearms get handled differently. Usually, particularly if I'm flying with long guns, (the cases of which are pretty obvious) the guns don't pop out onto the carousel. They will show up in the oversized baggage area and the nice TSA folk will hand them over once you've produced photo ID. Juneau AK was the best. EVERYBODY had guns.
Little handgun boxes usually show up with the rest of the luggage. Buy a good case though. Those airline guys are tough on stuff. Mine are aluminum and are badly scarred. (I think they use them for wheel chocks for the aircraft or something.)
Ammo has to be secured in a box. Usually 50 rounds max. If you need more, better to ship it to yourself at the final destination or make arrangements to buy it there.
I still get nervous though. That's a lot of money in those boxes and guns are naturally very attractive to thieves. Thus far though, no problems. I do sigh a deep breath of relief when I see the box though.
Have fun on your trip!