Unfortunately, no one knows the origin of the classification or number "NCC" or "1701" respectively. Only Gene Roddenberry would know that, and he is no longer with us unfortunately.
Please consult the Memory Alpha page NCC, and scroll down past the ship registry list to the "Background" section. There you will find some satisfactory explanations. CDRCasey 22:37, October 2, 2011 (UTC)