0.6 is fine if it is stable - there is no acceptable or unacceptable PSA threshold for a man on HT; it will vary from man to man.
When his chemo fails, they will usually offer abiraterone or enzalutimide, often it is down to the individual doctor's preference but is sometimes affected by whether the man has other medical conditions. If he coped well with the chemo first time round, they may offer it again, either docetaxel again or cabazitaxel the next time. We had a member here who had blocks of chemo 6 times because he tolerated it so well but that is very rare.