How to pick Hamming distance
The author of the list that you mention has written a thorough report on the problem of selecting a CRC polynomial, which probably contains the answers to all your questions. See page C-19:

Important to select CRC polynomial based on:

Data Word length
Desired HD
Desired CRC size

Safety-critical applications commonly select HD=6 at max message length

For example, HD-6 detects between 1-6 error bits in the Data Word, so the bigger the HD the better (for the given Data Word length).