I fly Sun Country with guns quite often, and I have looked at other airlines. They are all basically the same.
TSA requires that the gun be in a hard side case with keyed padlock. TSA will allow you to put the gun case in your main luggage, however, some airlines and airports will not allow you to do this if you have live ammo in your main luggage. TSA says you can carry up to ten pounds of live ammo, but some airlines and airports will limit the number of rounds (MPLS/STP will allow a max of 100 rounds regardless of weight). TSA has a set of rules as to how many guns can be in a single case, but some airlines will change and limit this (I flew west on Sun Country with five in one hard case with no problem, but when it was time to come home they only reason they let me through was that I could show paperwork that I had flown there that way).
Bottom line - Print out both TSA and Delta firearm requirements, and then call Delta at all airports you will be departing from and get their interpretation of the rules. Start a journal that contains all lists you print out, and record all conversation points including names, dates and times in this journal. This is not a guarantee that you will not have any problems, but it will help.
Other tips:
1. The ticket agents are scared to death of your guns;
2. TSA does have a sense of humor, but this is not a time to try it - lots of yes sir, no sir, thank you sir;
3. Do not carry your gun case from check in to TSA - the ticket agent must do this while you follow (one poor Sun Country employee is still walking funny from the chewing he got last winter when he made me carry the case);
4. Do not leave TSA until they tell you that your luggage has cleared their inspection (sometimes they just x-ray and sometimes they search) because they may need your keys or an explanation;
5. Once done with TSA, go directly to your gate for check-in, present them with your paperwork, and let them know where they can find you if they have any questions (about a third of the time they will seek me out for information, and the pilots like to see who is bring the guns on their planes);
6. If possible, watch while luggage is loaded on the plane - every time I have been able to watch my gun case has been set off to the side and loaded last;
7. Rush to the luggage claim area as soon as you can - you want to be their to grab your gun case as soon as it comes off;
8. Most airlines will tell you to come two hours prior to flight to check in, you will notice the check in goes really fast and wonder why not come later - don't, everytime I have been early the check in goes quick with no problem, and everytime I have been at the one hour point the check in and inspection gets to be more involved and uncomfortable;
9. Hint - This is not a day to show up in your grungies with a three day beard. Business casual will get you a long way fast.
Overall flying with guns has been no problem. It is just that everyone interprets the rules a little different. Do your homework, and it will go fine.
Have a good trip!