Nagano to Matsumoto

What JR line will I be taking from Nagano to Matsumoto? I have checked the JR east website and cannot find it. Can I not reserve the seat for that trip? Also, will I be able to reserve seats on the Shinkensen with an ordinary ticket

What JR line will I be taking from Nagano to Matsumoto?

The two cities are connected by the JR Shinonoi Line.

Can I not reserve the seat for that trip?

On limited express trains: yes
On local trains: no

Also, will I be able to reserve seats on the Shinkensen with an ordinary ticket

You cannot "make reservations"
with an ordinary ticket. Seat reservations are purchased separately from the base fare ticket together with the express supplement.

With a JR East Pass or Japan Rail Pass, seat reservations can be made for free.

Nagano to Matsumoto is connected by JR Shinoni Line as Uji said.

There are Limited Express (Tokkyu) trains called Wide View Shinano from Nagano to Nagoya, which stops at Mastumoto. You can make reservation for this train at any JR's Midori no Madoguchi at most major stations in Japan. This train is the same train you take if you are coming from Nagoya (from Kyoto and Osaka areas) to Matsumoto but the opposite direction.

You can try this link to map your itinerary, write it down and hand it over to the JR clerk at any train station.

http://grace.hyperdia.com/cgi-english/hyperWeb.cgi

Chad