Hi there,
The Japan Rail Pass is valid for all shinkansen except the Nozomi and Mizuho service. This means that for the journey to Kyoto from Tokyo you'll need to use the Hikari service. According to Hyperdia the difference in time between Nozomi and Hikari bullet services is 22mins (160mins on Hikari vs 138mins on Nozomi), so unless you are very time sensitive the journeys should not be too different (Hikari uses the same rolling stock as Nozomi, and reaches the same top speeds but stops at slightly more stations en route).
The Hikari has non-reserved and reserved seating, and Japan Rail Pass holders can make seat reservations for free. To make a reservation simply present your rail pass at the ticket office and specify the train you would like to board. In general I have found you can easily make reservations on the next available Hikari train and do not have to reserve far in advance unless you wish to travel during rush hour periods.
Hope this helps!