Here's what I did last April. After going through immigration and customs at Narita, I went downstairs to the JR office to get my Rail Pass. I asked them to start it 3 days from then. After doing this, I requested and got my seats on the Shinkansen for the day my Rail Pass starts. There's no extra cost to get a reserved seat.
The people in the JR office are very efficient and do speak English. So it is really not difficult to get reserved seats on the bullet trains. I would just do it at least a day or so ahead of time of your planned departure.