What consequences do the plaintext space size has on the performances in the BGV scheme? In the BGV paper [1], the authors say in §5.4 that you can have $\mathbb{Z}_p$ as plaintext size with a large $p$.

What is the impact of the size of $p$ on the ciphertext size and computational work of the cipher's algorithms?

I would need this to decide how big my plaintext space can be before it becomes impractical.

References

[1] Brakerski, Zvika, Craig Gentry, and Vinod Vaikuntanathan. “(Leveled) Fully Homomorphic Encryption Without Bootstrapping.” In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, 309–25. ITCS ’12. New York, NY, USA: ACM, 2012. doi:10.1145/2090236.2090262.
http://eprint.iacr.org/2011/277
A helpful resource to assess which ring-based FHE scheme (like BGV) would work best for you, see here: https://eprint.iacr.org/2015/889

In this paper they compare four schemes: BGV, FV, NTRU, and YASHE. 

The reason I point you there is that one major factor in the performance of these schemes is the value of p. If a large p is used, BGV outperforms the rest. If a small p is used, YASHE wins, but not by too much. The other main factor is the L parameter. 

The metric they use to compare them is the ciphertext size, which is crude but gives a rough estimate as to the computational time needed.