How do 2 different prepositions change the meaning of a tag line?

We cannot answer this for you. Both "to" and "of" can be properly used here, but impart different meanings to your tag line. Only you can decide which meaning is intended.

"Journey to" suggests the result of the journey is "hope and wellness" -- the journey itself may be full of dispair and sickness, but it has a happy ending.

"Journey of" suggests that the journey itself is characterized by "hope and wellness".

Let me suggest an analogy -- "Journey to Victory" versus "Journey of Victory". The first is the prelude to the race and the race itself -- we don't know who wins until the race is over. The second is the victory lap taken by the winner after the race.