These all make a difference. In the end, to be "elite", you would have to be good at all of them.
In the beginning, improving on any of these will help immensly.
For example, learing good breathing can get you away with having bad co2 tolerance, since you start with less co2 in the beginning. Same for O2.
How ever, you will soon reach a point, where you cannot improve any further with breathups alone, so you'll need to learn tolerance anyway.
From personal experinece I would say, that in the beginning, you get fastest results by trying to find out the correct warmup/breathup routine. Just be careful of hyperventilation and don't ever train in the water alone. And be aware that you will inevitably hit a wall. First make huge leaps in progress and suddenly halt...This is quite normal, you just need to change focus to another area of training...
A good starting point would be to do apnea in a series. I find it (and most others as well), that after doing a couple of easy statics, it keeps getting easier. Try for the max on say the 4th or 5th try, gradually increasing the amount of pre-breathing you do. You might want to try empty lung statics as well for warmup, since they really nicely kickstart the dive reflex. Keep the warmup holds easy though, save your will and strength for the big one. Hold the warmups just until the phase where you start to get clearly uncomfortable.
For a beginner, the static training tables can also be very useful.
