As someone said just do it whenever you're comfortable and will give max. effort. Doing it in the morning when half-awake wouldn't cut if for me either. Consistency and effort are more important than timing.
HIIT is good, as mentioned it would have to be tried for a month or so and keep the diet the same then compare. Some find it more effective, on the other hand others find that it's tough on the central nervous system because of the intensity, potentially higher chance of burnout. Just as when to do cardio, the choice of HIIT or longer less intense cardio is more about personal preference than differences in effectiveness.