How have common PRBS polynomials been chosen, and what are they?
The number of maximal-length sequence generators increases rapidly with the degree and so tabulating all of them is impracticable for large degree. A standard table of all irreducible binary polynomials of degree 16 or less (and a few selected polynomials of degrees up to 34) takes up 17 pages in in an Appendix of Peterson and Weldon's Error-Correcting Codes, (2nd ed.), MIT Press 1972 and they are much more densely packed than the prolix notation used in the OP's reference.  As to which ones are in common use or which have desirable properties, it depends on what is meant by desirable; mathematically, they are all equivalent, practically, there might be good reason to choose one over the other. One preferable feature might be small number of nonzero coefficients (which reduces the number of XOR gates (or instructions in software implementations).  Another might be smaller overall complexity of implementation: the primitive polynomial of degree 8 used in the Reed-Solomon code implementation in the NASA system was carefully chosen to minimize the overall complexity of the decoder (and no, it is not the first one in the Peterson&amp;Weldon table).