What would be a typical value for the security parameter of the Fully Homomorphic Encryption over the Integers scheme?
For the first part of the question, I couldn't find where the authors Quantify their security, what I understood that they build their scheme based on the hardness of GCD problem.

As for the second part, According to NIST recommendation which is a non-regulatory federal agency within the U.S. Commerce Department's Technology Administration. a secure value is estimated to be 112 and this won't be broken before 2030.  For other security estimates according to different schemes you can refer to https://www.keylength.com/