The "-ise" spelling is the one usually given as primary by the Cambridge dictionary, while the Oxford dictionary prefers "-ize". Oxford's reason for this is etymological. They give an interesting explanation under the entry -ize. I attach a snapshot below.
Edit: in summary, many of these verbs come from Greek forms corresponding to "-ize", and the change to "-ise" came later through French. The Oxford Dictionary people don't see why the French derivative should be preferred to the original form. As a consequence, they use "-ize" for verbs that have that etymology, but not for others: for instance the dictionary gives realize but also analyse, because the latter doesn't have the Greek "-ize" etymology.
Great advice, thank you! I'll give a first try to the first three through live disks :)