I tend to go toward Redemption, maybe because of the vagueness of it. As was said, one can't simply fix the colossal mistake Lanriel made, but she should certainly want to try - even if the road ahead seems impossible, or even if she has no idea who she's seeking redemption from - the Phoenix Throne, her companions, herself, the Gods?
Fresh Start sounds maybe a bit too calous to set as a goal straight away - it can be interpreted as a way to brush things aside and not look back on what happened - which is certainly tempting, and perhaps even healthy in some way, but maybe not a state of minde Lanriel should feel right now.
Return to Ulthuan kind of seems the worst answer - as other have pointed out, it seems to brush aside what forced her to leave in the first place. Killing Chaos might be a tad too bloodthirsty. Nothing against Making Up for Crimes - which is quite close from Redemption - but it sounds maybe a little too transactional to my ears.
Anyway, here's my two cents about the topic. Really enjoyed this update, and the rest of the quest so far, and I can't wait to see how it will develop!