There are many shipping companies available. Nippon Express was in fact the largest freight forwarder in the world, measured by revenue, however, believe that now too belongs to Sinotrans.
I used a local freight forwarder for packing and shipping my stuff to Japan to Yokohama port. I arranged Yokohama port to my home with MovingJapan.com (owned by a company called Vancombe Inc)
Ref your questions about import of personal affects, MovingJapan.com has a moving guide here -->
MovingJapan.com - Moving Guide
Good luck!