For example, on Bench Press do as many reps as your body allows and then keep trying after that, and if you move the bar that counts as a rep. The 3 other types of failure, concentric, eccentric, and static, would all occur on the way to your description of absolute failure. You are done when the bar is on the pins. What is best for you is the path that allows you the quickest progression over time. If you train to absolute failure in order to add 5 pounds to a lift in 14 days, that would not be as beneficial as training 1 rep shy of failure and adding 2.5 pounds every 5 days.
Personal preference is also relevant here.
You have to be able to make gains over the long term, so enjoying your training is going to be an important issue. I would guess that the harder you train the biggest lifts, the faster you will be capable of gaining. I have a question. I've got weak back development, compared to other parts. I go to momentary muscular failure on all lifts, but see little improvement.