At the US postal service, your choice is usually between sending something by "regular mail" or by "express mail." You will be understood by using "ordinary," but "regular" is the usual term of art in this context.

I think you would be understood. "Normal" shipment is presumed to be the default method of shipment. "Express" shipment implies shipment by a faster means, usually by air, to arrive more quickly. I hope that this explanation helps.