Because of the far away location from airport, even most Japanese in Tokyo take Shinkansen instead of flights when visiting Kyoto anyway.
Shinkansen Nozomi, departing every few minutes, takes only 2 hours from Shinagawa(Tokyo) to Kyoto directly.

Shinkansen allows at the most two luggage within 250cm(98 inches) total dimension: larger than checked baggage acceptable size.
There is enough space for luggage in Shinkansen at the behind of the last row in front of the bulkhead of each car.
You may reserve the last row or wheelchair space(row12-13 at Car11) nearby; nowadays ticket vending machine shows seat map.
Most people taking Shinkansen with luggage do so.