I am looking for the best word for a person who is continually moving from place to place without good reason, job or fixed home.
Drifter is probably the best fit here, as it doesn't have too many connotations, as nomad, vagabond, and itinerant do.
Naturally, it must be added that the context will ultimately determine the best word-choice. Tramp, nomad, vagabond or even adventurer might well be better words; the choice depends on your specific situation.
I remember the word from Julian Assange's trial
The judge expressed his own concerns over Assange's rich and powerful supporters, like Australian documentarian John Pilger... The one laugh at the hearing this morning came when the judge scoffed at using Pilger as a surety since he was just "another peripatetic (italics added) Australian." Even Assange cracked a smile at that one.
It has so become associated with a popular musical group that nobody mentioned:
Definition of rolling stone in English:
A person who is unwilling to settle for long in one place.
‘he was a rolling stone, with no ties to anyone or anyplace’
(Although I personally do not condone the Oxford English Dictionary's use of ‘any place’ in an example.)