What is the error-detection-probability of CRC
There's nothing in your requirements that forces you to use a CRC32.  You could use any checksum.  If the collision probability for a CRC32seems too high, use a different checksum.

For instance, if you use SHA256, you will never have to worry about collisions -- for all engineering purposes, you can treat them as impossible (something that will never happen in your lifetime).  And then you won't need to worry about selecting generator polynomials or anything like that; someone else has done all that work for you.  You just use the standard SHA256 algorithm.



P.S. Using a basic checksum algorithm will require you to recompute the checksum on the entire table any time you insert or delete one row.  If that's too slow, there are a number of schemes to speed that up, such as a Merkle hash tree.