Every classical guitarist needs either a footstool, guitar support or a cushion to be able to sit in the playing position. This is important, especially if you practice very often, as an incorrect sitting position might cause back problems over the years.
Many classical guitar pieces, especially a large portion of renaissance and baroque repertoire, might also require a guitar capo, so make sure to always have one in your guitar case.
We'd also recommend having a guitar tuner. In certain rooms and venues, it's harder to tune a guitar. In such situations, a guitar tuner might be very helpful.
If you play in front of others and need sheet music, make sure to put it on a music stand. Reading from sheet music put on a floor or a chair might distract listeners from your playing.