Ship it in the case. FedEx does this all the time. I have wrapped the outside of a mixer rack case with cardboard to help prevent road rash, but you don't need to go crazy, and don't cover up the handles and wheels. Just put some extra padding around the amp so it doesn't move around inside the case.
It helps if you take big and/or heavy items to an FedEx Authorized Shipping Center. These are usually the big places close to railroad access with lots of trucks, etc. But you can also drop it off at most Mailbox, Etc. type stores, as FedEx and UPS pick up at those places at least once a day, often around 5 pm.
You can go to the FedEx website and get a free account, which will also get you a discount, and bill it to a credit card. You can do all your shipping on the website, print out shipping labels, and set up automatic emails to inform the buyer. FedEx tracking is very good, better than USPS Priority. UPS tracking is good, too. UPS, FedEx, and USPS all have calculators to estimate shipping charges. You just plug in the size and weight numbers, and the Zip codes.
If you remove the tubes, make sure they are individually wrapped so that glass does not touch glass. I would leave them in their sockets, unless the sockets or retainers are loose. Mesa ships new amps with the tubes installed.