I moved over two hunderd guns myself, in our last move. We used a rented truck and moved them all at once, in cases or boxes as best we could pack them. Now I would have much more to move but would do it the same way again.
If money is not a problem, I would have them shipped by sealed container, point to point. Make sure that the carrier is insured and that they can and will handle guns. Some companies get a little funny when you mention large sums of money and guns in the same breath. It would be delivered to your new house and you should arrange to be there when it arrives. Best to have your new storage ready and move guns out of container and directly into the new safes, gun room, or other storage areas.
Most trucking companies would quote you a rate for sole use of one of their trucks to ship your guns. Let them know what you want and amke a few calls. With fuel high any trucking company that is dead hauling might jump at the chance to make more money if it does not mess with their regular bussiness. I shipped 30,000 board feet of lumber to my brother in FL via a dead hauling truck and paid 150% of the fuel cost. It saved me several thousand dollars in freight and got the wood directly to my brother for far less than he could have ever bought lumber locally for furniture building.
As the kids say think outside of the box.