In spring season, the busiest period is late April and the beginning of May. It is called “Golden Week” in Japan. April 29, May 3, 4, and 5 are National holidays. If you can, lease try to avoid travelling on those days.
Fall is good season to travel in Japan. JR Group operate lots of seasonal trains during this season. But it is too many to introduce all seasonal trains. So I pick up the popular trains and are operated in the popular spot.