The best advice I can give is to get a FedEx or UPS account or try to ship through something like Pirateship.com. Never pay full retail as you will get hammered. Actual weight won't kill you but dimensional weight will. Anything over 48" (as mentioned above) gets hammered. I buy boxes from amazon that are 4"x8"x46". My average long gun shipment is under $25 in the CONUS not counting packaging or insurance.

Insurance is smart if you are just shipping a few guns now and then. However, if you ever actually have to file a claim you will learn that the insurance people (for any of the carriers) full time job is to make sure you DON"T get paid. I ship enough guns that it has made more sense to simply open a savings/investment account and put a few bucks into the account for every gun I ship and just self-insure. Actual damage is very rare if guns are packaged properly. The only claims I have had after many 100s of guns shipped were a couple of cracked stocks that I was confident weren't that way when they shipped out. Since I am the insurance company it is way easier to handle claims with offers to return, repair or settle for cash. I have been able to keep buyers happy and not drag things out for weeks waiting on insurance settlements.

One horror story...a good friend is a custom rifle builder. He built a high end rifle off of a new Rem 700. Insured it for the full sales price of the custom ($4-5K if I remember correctly). UPS or Fedex truck rolls and bends the rifle...no question they caused the damage. They only pay him $700 to cover the retail cost of replacing a Rem 700 at the time. So he is out the difference despite paying extra for full insurance on this and many other rifles.