You will only have to pay for your airfare, tips and additional shells. Before your departure from your country you will have to pay the reciprocity fee if you are travelling from Canada or Australia. Remember that gun rental is included but if you decide to bring your own gun you will have to pay for importation.
United States: If you are traveling with guns, you should pre-register each gun taken out of the country. U.S. Customs Form 4457 is the one you will need to fill in, it is a certificate of registration for personal effects taken abroad. You will need to present your firearms for this procedure at any U.S. Customs office, at least one week before your trip. Please keep the original Form with your passport and put a copy in your gun case. This regulation applies only for re-entry into the United States. You will also need to check with the airline once you have your itinerary as they all have different regulations regarding traveling with guns.
Rest of the world: You will need to check with your country and also the airlines to see the regulation for traveling with guns.