When you go to southern part of Nagano from Nagano, the Limited Express Azusa is most convenient choice. You can get Matsumoto directly. And one trip of this train takes you to Hakuba and Shinano-Omachi directly.
The Limited Express Kaiji runs on the same route between Kofu and Shinjuku/Tokyo.
And the new train, “FUJI EXCURSION (Fuji-Kaiyu)” has been introduced in March 2019. This train connects Shinjuku and Kawaguchiko (Lake Kawaguchi at Mt. Fuji) directly.
I will explain you the route, schedule and accommodations of these trains.