I won’t rehearse everything that being said over on the JAL thread except to say from my limited experience I would go Shinkansen unless I was really chasing tier points.
I would be fine with a reserved ordinary car ticket. You will want to look into a Japan Rail Pass anyway if you are planning on using the Shinkansen and other trains during your trip.
While not essential to use the luggage courier service I probably would. Be aware it might not arrive at your hotel until next day so you will want an overnight bag. Yamato is ubiquitous (
Traveling to Japan | YAMATO TRANSPORT GLOBAL) and I think there is a JAL branded option too at NRT. No need to pre-book pay just go to the desk in arrivals.