Hi Mitsokim,
It cannot choose to move first. As soon as the Bloodthirsty creature is activated, you check 2 conditions:
1. Is there a damaged enemy creature in his zone?
2. Can he attack that creature? (For example, the damaged creature might be flying, or there might be a guard in the zone which would redirect his attack.).
If the answer to both questions is YES, then he must make a melee attack on the enemy creature.
If the answer to either question is NO, then he can choose another action. However, if he moves to a new zone, he must immediately check the same 2 conditions for that zone as well.