Call the center and ask. They can help you with contacts in town.
We usually stay on the property -- there are several levels of accommodations available.
Flying with rifles isn't all that complicated. You just have to worry about the bag apes smashing your guns!
Basically, make certain the rifle(s) go into a GOOD case -- NOT one of the $50 specials!
Plan to arrive a little early at the check-in counter.
Be prepared to show the counter agent (who won't understand anyway) that the rifle is empty.
Sign the form certifying that it's unloaded, put the form INSIDE the case and take it to TSA. They'll want to check it over again and then they'll relock it and send it on its way.
IMO it's best NOT to ship ammo in the case with the rifle. (TSA says it's OK to ship in the same case but many airlines want ammo in separate baggage.)
The ammo must be in either original factory packaging or in approved ammo boxes and the limit is 5 Kg or 11 lbs. I prefer to put it into a lockable, hard suitcase. After TSA inspects that bag, they'll mark and lock it just as they did the gun case...so it shouldn't be broken into again by the 'inspectors'. But that's not cast in stone. (You can buy TSA approved locks that they can open without destroying.)
Unless you fly with an airline with which you have a 'history' -- so that you know their policies -- you probably would be well advised to call the airline and ask about their policies on firearms.
I 'think' -- but I'm not certain -- that most airlines will not accept more than 2 firearms per passenger.
I don't worry about extra insurance but many like to purchase it. If that's your plan, arrive PLENTY early since most counter agents are unfamiliar with additional insurance and it goes slooooooooooowly. IIRC, basic domestic airline coverage -- before any added insurance -- is $2600 per bag; but that info may be incorrect.
Do yourself a favor: DOUBLE check ALL your pockets for loose ammo. You can't have any loose rounds in your shooting vest in your baggage and you DON'T want any to show up at security in your carry-on or on your person.
Leave your cleaning solvents at home.
You can detach your scopes and carry them through in carry-on bags at MOST airports. Ditto the spotting scopes, etc. 'SOME' security types interpret the "no firearms or firearms PARTS may be carried on board" very literally but most of them allow optics to be hand carried.