Cases shipped via UPS Ground should not cost $20-$30, unless it's a server case. Most Mid-Tower cases should only be $15 or less shipped via UPS Ground (Cheapest way). (That's assuming the case is empty. If your sending a full system in case, that's a different story)
If you are sending a full system in a case, I would recommend you to double box it up, and send it with
insurance. Also, don't send it with UPS since they tend to screw things up.

(This is assuming there's a system with that case

)