Shipping 2 shotguns and 8 rifles
So, there are two ways to do this as far as I know, but maybe someone knows of others.
1) use individual cardboard boxes for each, and pay separate shipping cost per box.
2) use a sturdy plastic or wooden crate to ship all 10 guns together, and pay for the single crate to ship.
A case from pelican for 10 long guns will cost $1,000+ retail. I wouldn't go that route unless you think you have a need to transport that many guns several times a year.
A wooden crate might be available from a packing/moving company. They can even make custom crates. I have no idea on the cost.
When considering shipping cost, a crate that size may limit your options. FedEx, UPS and USPS have limits on the size and weight of items they'll accept for normal shipping. You may have to go with a freight company.
Another thing is how protected the guns will be. Guns stored in crates sometimes get damaged. Packing them individually in separate boxes sounds like a safer method to prevent damage. I can see someone dropping a big crate and damaging several guns, where a single well-packed box would protect better when dropped, as the weight of one gun is much lighter than 10 guns + the crate.
10 guns at about $40 per gun, individually boxed, is $400. That would be my lowest estimate for this. Most long guns I've had shipped here were $40-$60 for shipping.